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THE  NATURE  OF  MUSIC 


ORIGINAL  HARMONY  IN  ONE  VOICE 


BY 

JULIUS    KLAUSER 


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COPYRIGHT,   1909,   BY   L,    E.   KLAUSER  <^  ^  — j 


ALL  RIGHTS   RESERVED 


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PREFACE 

This  work  was  originally  planned  in  two  parts,  but 
only  six  chapters  and  one  section  of  Chapter  VII  which 
was  to  conclude  Part  I,  were  written  at  the  time  of  the 
author's  death,  Monday,  April  22,  1907. 

The  one  section  of  Chapter  VII  has  been  omitted 
from  the  book  because  it  was  not  left  in  the  form  in 
which  it  would  have  been  published.  The  title  of  the 
chapter  is  "Potential  Harmony  of  Melody.  Expan- 
sion of  Tonality.  Chromatic  Harmony.  Modulation." 

Asterisks  in  the  manuscript  have  been  preserved  in 
the  text ;  they  indicate  where  footnotes  were  to  have 
been  supplied. 

Dates  in  the  manuscript  show  that  Chapter  III  was 
finished  during  September,  1904,  and  Chapter  IV 
April  9,  1905. 

These  six  chapters  unrevised  are  published  as  they 
were  left,  with  one  exception.  To  make  space  for  the 
examples  on  page  238  a  sentence  has  been  omitted.  It 
reads, "Thus  the  full  thorough-bass  index  of  the  above 
terce-form  would  be  ^  of  which  6  is  the  abbreviation." 

The  Bird-songs  published  as  an  appendix  were 
probably  not  intended  to  form  a  part  of  the  book,  but 
I  wish  to  preserve  them  and  they  may  be  of  interest. 
Twenty-five,  Nos.  62-86,  are  entitled  "Birds  of  Idle- 
wild  1903,"  however  with  the  exception  of  a  few  from 
Silver  Lake  near  Oconomowoc  most  of  these  songs 
were  heard  and  recorded  during  several  summers 
at  Idlewild   near  Sturgeon  Bay,  Wisconsin.   In  the 


vi  PREFACE 

manuscript  Nos.  1-9  and  43-86  were  written  on  the 
staff,  but  Nos.  10-39  were  indicated  only  by  sylla- 
bles and  40-42  by  letters,  in  consequence  of  which 
the  pitch  of  these  songs  is  not  quite  certain. 

To  Miss  Luise  Haessler  I  wish  to  acknowledge  my 
thanks  for  the  help  she  has  given  me  in  copying  most 
of  the  examples,  all  of  the  bird-songs  and  in  supplying 
a  paragraph  of  explanation  page  254  and  three  ex- 
amples pages  230-252. 

L.  E.  K. 

WiLLiAMSTOWN,  MASSACHUSETTS,  June,  1909. 


CONTENTS 


CHAPTER   I 

Introducing  First  Principles 

SEC.  PAGE 

1.  Qiiestions 1 

2.  Homophony  or  Mime  in  One  Voice 4 

3.  Origin  of  Music 6 

4.  Music-Feeling,  the  Source  and  Fountain  of  Music. ...  8 

5.  Cause  of  Union.    Shaping  Principle 10 

6.  World-Energy 11 

7.  World-Rhythm.     Universal  Form 12 

8.  World-Harmony.     Universal  Principle  of  Form  and 

Relation 12 

9.  Cardinal  Principle 15 

10.  One  Music 15 

11.  Rationale  of  Mu^ic 17 

12.  Common  Reports  of  Common  Feeling 17 

13.  Elemental  Form 22 

14.  Elemental  Relation 22 

15.  Melody,  a  Composite,  not  an  Element 23 

16.  The  Efficient  Accent  and  Regnant  Harmony 24 

17.  Principle  of  Potential  Harmony 26 

18.  Basis  of  Verification 27 

CHAPTER   II 

Rhythm  and  Tone 

19.  Definitions 30 

20.  Analysis  of  Rhythm 31 

21.  Analysis  of  Tone 33 


viii  CONTENTS 

BEC.  PAGE 

22.  A  Toners  Harmonic  Thread 35 

23.  Harmony  in  One  Voice.     Common  Reports 36 

24.  Harmonic  Evolution.     The  Major  Tonic 40 

25.  Rhythm-Cadence  and  Rhythm-Repose 42 

26.  Tone-Cadence  and  Tone-Repose , 45 

27.  Melody,  Harmony  and  Rhythm 48 

CHAPTER   III 

Original  Dissonance  and  Consonance  in  One  Voice 

28.  Genesis  of  the  Major  Consonance,  Musics  First  Reg- 

nant Harmony 53 

29.  Genesis    of   Cadence-Harmxmy  or    Original    Disso- 

nance in  One  Voice 61 

30.  Distinction  between  Original  Harmony  in  One  Voice 

and  Chord-Harmony 68 

31.  The  Seven  Original  Tones.     Analysis 75 

32.  On  Symbols 86 

33.  The  Five  Components  of  Harmony 89 

34.  The  Five  Original  Cadences.     Mode  Defined 91 

35.  Progression  and  Resolution 96 

36.  A  First  Music-Lesson 98 

37.  Work  for  Students 101 

CHAPTER   IV 

The  Efficient  Accent  and  Regnant  Harmony  of  Melody 

38.  Regnant  Harmony  in  One  Voice  and  Its  Principle  of 

Genesis  Explained 102 

39.  Chords  Derived  from  the  Original  Consonance  and 

Dissonance  in  One  Voice 133 

40.  The  Tone-Region.     Its  Diatonic  Scales 141 

41.  Musical  Moments.     Power  and  Originality  of  Music  149 

42.  Subrhythm  and  Rhythm-Expansion.    Music's  Classic 

Form 160 


CONTENTS  ix 

CHAPTER  V 

Obigin  and  Nature  of  Minor 

BBC.  PAGE 

43.  Origin  of  the  Minor  Consonance 176 

44.  Original  and  Duplicate  Forms  of  Harmony 184 

45.  Origin  in  One  Voice  of  the  Minor  Form  of  Disso- 

nance.    Original  Cadences  of  the  Minor  Mode . . .     185 

46.  Three  Regnant  Minor  Harmonies  and  Their  Bytones 

and  Cadences 198 

47.  Harmonic  Percepts  of  Minor  Origin 222 

48.  A  Toners  Harmonic  Pedigree 224 

49.  Chords  Derived  from  the  Minor  Forms  of  Consonance 

and  Dissonance  in  One  Voice 231 

CHAPTER   VI 

Chords  in  the  Light  of  Their  Origin 

50.  Description  and  Summary  of  Chords  Thus  Far  De- 

rived      237 

51.  Simple  and  Compound  Chords  Defined 243 

52.  Melody  the  Original  Reporter  of  Harmony,  Therefore 

the  Natural  Preceptor  and  Guide  in  the  First  Studies 

in  Chords 277 


Bird  Songs 291 

Explanation  of  Symbol  Numbers 305 

Index 307 


CHAPTER  I 

INTRODUCING  FIRST  PRINaPLES 

1.   Questions 

Science  has  not  yet  fathomed  the  mystery  of  the 
prigin  and  early  evolutional  stages  of  music.  Our 
knowledge  of  the  evolution  of  music  is  confined  to  the 
records  of  a  few  thousand  years  of  history.  Its  his- 
tory plainly  shows  that  music  has  passed  through  pro- 
gressive stages  of  evolution  from  simplicity  to  com- 
plexity. But  how  it  began  far  back  in  the  ages,  the 
causes  of  its  genesis,  its  shaping  energies  and  forces, 
its  essential  nature,  these  and  like  questions  still  wait 
for  a  scientific  solution.  Sound  emerges  from  and 
evanesces  in  silence.  We  assume  that  incalculable 
ages  ago  there  was  a  time  when  music  as  yet  unborn, 
unheard,  lay  dormant  in  silence,  a  mere  potentiality. 
The  evolutional  study  of  music  therefore  begins  with 
silence.  All  that  is  music  is  potential  in  and  an  evolu- 
tion of  an  embryo,  namely,  the  composite  of  elements 
upon  the  genesis  of  which  depended  the  genesis  of 
music.  What  is  this  composite.?  ^Vhat  are  its  ele- 
ments ?  What  is  the  principle  or  cause  of  their  union  ? 
Where  and  how  did  and  does  this  union  take  place.? 
These  are  leading  questions  which  confront  us  in  this 
study.  We  investigate  melody,  rhythm,  harmony,  to- 
nality, the  tone-realm  or  tone-system.  What  are  all 
these  things  ?     What  is  the  origin  and  nature  of  each  ? 


.^,  I }.  'I  < ' :         THE  NATURE  OF  MUSIC 

Which  are  elements  and  which  are  composites? 
Which  is  the  original  and  all-inclusive  composite? 
the  raison  d'etre  of  all  the  others,  in  short,  the  essence 
of  music?  Theoretical  predilections  or  subjective 
bias  cause  some  of  us  to  give  the  supremacy  to  melody, 
others  to  harmony.  We  still  speak  and  write  about 
"the  intimate  connection  between  melody  and  har- 
mony, "  about  " harmonized  melody"  and  " melodized 
harmony."  All  this  plainly  implies  a  common  belief 
that  melody  and  harmony  are  separable.  Are  they, 
have  they  ever  been  separable  or  separated  ?  If  not, 
one  of  the  two  is  an  element  of  the  other.  In  fact,  one 
of  the  two  includes,  is  the  raison  d'etre  of  the  other. 
Which  is  it  ?  Science  has  produced  no  final  answers 
to  these  questions.  Let  any  one,  musician  or  layman, 
consult  the  testimony  of  his  unprejudiced  inner  feel- 
ing and  experience  of  music  and  he  will  say  with 
Mozart,  **  Melody  is  the  essence  of  music."  I  quote 
Mozart  because  he  was  completely  free  from  theoreti- 
cal bias.  He  felt  and  knew  this  to  be  true,  he  felt  and 
knew  it  instinctively  just  as  we  all  do.  In  other 
words,  the  truth  of  this  common  testimony  of  com- 
mon feeling  has  not  been  scientifically  proved.  Nor 
has  it  been  disproved.  Why  not  ?  Primarily  because 
the  nature  of  its  source,  that  is,  the  nature  of  common 
music-feeling,  has  not  been  fathomed.  Yet  the  exist- 
ence of  this  common  feeling  is  everywhere  recognized 
in  the  books,  this  feeling  is  the  source  of  every  truth 
that  has  entered  the  books,  its  testimony  is  every- 
where appealed  to  and  is  our  only  resource  in  every 
last  analysis  wherever  and  whenever  rules  fail  to  apply 
or  cannot  be  ascertained.    The  situation  has  a  pe- 


INTRODUCING  FIRST  PRINCIPLES  S 

culiar  interest.  We  all  share  in  this  common  feelings 
yet  do  not  succeed  in  translating  it  into  common 
thought,  do  not  succeed  in  expressing  it  in  so  many 
words.  Unless  this  can  be  done  it  will  be  impossible 
to  answer  any  of  the  above  questions.  If  it  really  be 
true  that  melody  is  the  essence  of  music,  the  original 
and  all-inclusive  composite  of  music's  elements  and 
principles,  then  it  is  also  true  that  melody  is  the 
raison  d'etre  of  harmony,  in  other  words,  that  har- 
mony is  and  from  the  beginning  always  has  been  an 
element  of  melody.  I  shall  endeavor  to  demonstrate 
in  the  following  pages  that  this  is  true.  But  how 
can  it  be  true  ?  It  is  flatly  contradicted  by  the  entire 
history,  theory  and  practice  of  music.  All  the  books 
teach  us  that  melody  antedates  harmony  by  unknown 
ages  and  that  harmony  was  discovered  and  introduced 
only  a  few  centuries  ago.  Is  not  this  evidence  con- 
clusive, final,  insuperable.^  Here  let  us  ask  a  plain 
question.  What  do  the  books  or  authorities  mean  by 
harmony  ?  Without  exception  they  mean  chords,  that 
is,  combinations  or  concords  of  several  tones.  No 
other  form  or  conception  of  musical  harmony  has 
thus  far  appeared.  To  speak  of  harmony  is  to  speak 
of  chords.  To  study  harmony  is  to  study  chords. 
Every  treatise  on  harmony  is  a  treatise  on  chords.  It 
is  the  common  belief  and  teaching  over  the  whole  musi- 
cal world  that  the  chord  is  the  one  and  only,  therefore 
by  implication,  the  original  form  of  musical  harmony. 
The  evolutionist  has  the  hardihood  to  question  the 
truth  of  this  common  belief  and  teaching,  he  does 
not  regard  the  complex  chord  as  a  spontaneous  gen- 
eration, he  reasons  that  so  complex  a  form  as  the 


4  THE  NATURE  OF  MUSIC 

chord  is  rooted  in  and  evolved  from  antecedent  sim- 
pler forms  of  harmony,  that  the  development  of  har- 
mony is  a  progressive  evolution  from  simple  to  com- 
plex which  began  with  the  genesis  of  music  in  one 
voice.  This  explains  the  subtitle  of  this  book,  "  Ori- 
ginal Harmony  in  One  Voice."  Everything  hinges 
on  the  question  of  the  origin  and  nature  of  music's 
specific  forms  of  harmony,  that  is,  of  consonance  and 
dissonance.  All  harmonists  know  that  this  ques- 
tion still  remains  unanswered.  A  single  obstacle  has 
stood  in  the  way  of  its  scientific  solution,  namely,  the 
prevailing  chord-idea  and  chord-view  of  harmony 
based  on  physical  acoustics.  The  age  of  the  chord 
reaches  back  a  few  centuries.  The  age  of  harmony 
reaches  back  through  all  the  ages  to  the  genesis  of 
music  in  one  voice.  The  development  of  original 
harmony  in  one  voice  occupies  the  entire  period  of 
homophony,  the  first  and  longest  evolutional  chapter 
in  music  and  the  most  important  chapter  for  scientific 
research- 

2.   Homophony  or  Music  in  One  Voice 

The  term  homophony  is  used  in  these  pages  strictly 
in  the  sense  of  music  in  one  voice  or  part  as  distin- 
guished from  polyphony  and  chorded  music  in  several 
voices  or  parts.  The  material  for  the  evolutional 
study  of  homophony  is  complete.  We  find  it  in  the 
simple  songs  of  birds  and  primitive  man,  in  ancient  and 
mediaeval  melodies,  in  folksongs  and  dances,  in  modern 
music  down  to  our  own  time,  for  the  works  of  all  the 
great  composers  contain  countless  motives,  phrases 
and  passages  in  one  voice.     Thus  homophony,  the 


INTRODUCING  FIRST  PRINCIPLES  5 

form  in  which  music  first  arose,  survives  to  this  hour. 
In  essence  and  trend  there  is  no  difference  between  the 
homophony  of  to-day  and  that  of  all  the  past,  between 
that  of  a  song-sparrow  and  that  of  Bach,  Mozart, 
Beethoven  and  Wagner.  We  here  confront  facts  of 
prime  importance.  Homophony  is  the  one  and  only 
form  common  to  all  music  past  and  present.  Homo- 
phony  is  therefore  the  one  and  only  tie  connecting  all 
music  of  all  time.  Nowhere  but  in  homophony  can 
we  study  and  discover  origins,  first  principles  and 
causes,  the  energies  and  forces  from  which  music 
proceeds,  the  incipient  stages  of  progressive  evolution 
from  tone  to  tone,  relation  to  relation,  harmony  to 
harmony,  in  self-fulfilment  of  inherent  laws,  in  short, 
nowhere  else  can  we  find  the  explanation  of  the  essen- 
tial nature  of  music  and  of  common  music-feeling. 
Hence  the  importance  of  homophony  as  a  field  for 
scientific  research.  Homophony  presents  and  verifies 
its  facts  in  a  most  unique  and  convincing  manner  since 
its  reports  completely  exclude  personal  prejudice  and 
eliminate  the  personal  equation.  The  personal  ele- 
ment of  choice  and  bias  did  and  does  not  enter  into 
music  until  a  second  voice  or  part  was  and  is  added  to 
a  first  voice  or  part,  that  is,  until  we  add  other  voices  to 
a  given  melody.  Homophony  discovers  this  remark- 
able psychological  fact.  Its  reports  are  self -reports, 
that  is  to  say,  they  are  not  what  you  and  I  or  ten  thou- 
sand others  may  think,  elect  and  debate,  they  are 
what  homophony  itself  elects,  asserts  and  reports. 
These  self -reports  are  common  to  all  of  us,  they  are  the 
common  reports  of  common  feeling  and  apperception, 
moreover,  they  are  immutable  and  discover  the  funda- 


0  THE  NATURE  OF  MUSIC 

mental  dat^  of  music  and  music-feeling.  In  the  field 
of  homophony  all  investigators  therefore  stand  on 
firm  and  common  ground ;  here  we  set  out  with  a  com- 
mon point  of  view  and  may  join  in  a  common  purpose, 
namely,  the  translation  of  self-reports  into  the  simple 
words  of  common  thought.  By  nature  we  are  all 
homophonists ;  the  music-consciousness  has  its  awak- 
ening in  homophony;  we  sing  and  whistle  homo- 
phony;  each  of  us  has  the  power  within  himself  to 
produce  and  reproduce  in  feeling  and  thought  any 
homophonic  melody ;  each  of  us  may  observe,  study  and 
analyze  homophony  at  his  leisure  in  himself  and  in 
others  and  may  learn  to  translate  its  self-reports  into 
words;  each  of  us  may  verify  these  reports  in  himself 
and  others;  in  short,  the  study  of  the  psychology  of 
homophony  lies  within  the  reach  of  every  musical  lay- 
man. The  conditions  for  the  evolutional  study  of 
homophony  are  favorable  for  another  reason.  The 
awakening  of  music-consciousness  and  the  evolutional 
sequence  of  tones,  relations  and  harmonies  in  the  de- 
velopment of  each  individual  musical  mind  corre- 
spond with  the  genesis  and  early  developmental  stages 
of  music  itself.  Supposing  then  that  the  material  re- 
presenting the  early  stages  of  homophony  did  not  exist, 
we  could  reproduce  that  material  by  tracing  the  psy- 
chological development  of  the  musical  mind  from  tone 
to  tone,  relation  to  relation,  harmony  to  harmony. 

3.    Origin  of  Music 

The  origin  of  music  is  due  to  the  union  of  two  ele- 
ments. The  two  elements  are  rhythm  and  tone. 
Rhythm  was  intoned,  and  forever  after  there  was 


INTRODUCING  FIRST  PRINCIPLES  7 

music.  Let  any  one  intone  a  simple  rhythm  and  he 
will  then  and  there  unite  the  two  elements  and  engen- 
der music  in  its  original  form  of  homophony.  What 
is  intoned  rhythm  ?  Simply,  tone-rhythm,  the  original 
and  indissoluble  composite  of  music's  elements  and 
principles,  the  embryo  in  which  all  that  is  music  is 
potential.  What  is  rhythm  ?  Universal  form  of  mo- 
tion. What  is  tone.^  The  specific  form  of  sound 
peculiar  to  music.  What  is  this  specific  form  ?  Har- 
mony of  sound,  in  one  word,  harmony.  In  music,  a 
tone  is  and  always  has  been  a  harmony.  We  shall  see 
that  the  harmonies  of  music  are  the  harmonies  of  rela- 
tions, that  they  assume  one  of  two  forms  peculiar  to 
music,  namely,  the  form  of  consonance  or  that  of  dis- 
sonance. The  original  forms  of  consonance  and  dis- 
sonance had  their  genesis  in  one  voice,  that  is,  they  arose 
in  homophony.  Thus  when  we  intone  rhythm,  each 
tone  that  we  express  is  one  or  the  other,  a  consonance 
or  a  dissonance.  This  is  true  of  every  tone  in  the 
homophony  of  birds  and  man.  Subsequent  analysis 
will  show  that  the  genesis  of  music  depended  on  the 
genesis  of  its  first  harmony.  The  first  harmony  is 
the  perfect  or  major  consonance  which  we  call  the 
tonic.  Let  any  one  rhythmically  reiterate  one  and 
the  same  tone  thus :  M  T  M  f  *  I  ^  etc.  He  will 
then  and  there  engender  and  express  the  first  har- 
mony which  far  back  in  the  ages  emerged  from  silence 
and  announced  the  genesis  of  music.  At  bottom, 
music  per  se  is  tone-rhythm.  At  bottom,  our  common 
feeling  of  music  is  the  feeling  of  music  per  se,  that  is, 
the  feeling  of  tone-rhythm.  As  we  proceed  let  us 
bear  the  following  points  in  mind.     In  music,  tone  is 


8  THE  NATURE  OF  MUSIC 

not  separable  from  rhythm.  All  relations  of  tones 
are  tone-rhythmic  relations.  All  forms  of  tones  are 
tone-rhythmic  forms.  Music's  specific  original  forms 
of  consonance  and  dissonance  could  not  arise  apart 
from  rhythm.  These  original  forms  lie  at  once  at  the 
foundation  of  music  and  of  common  music-feeling. 
In  our  common  feeling  of  music  itself,  as  just  defined, 
let  us  seek  to  discover  the  true  nature  and  funda- 
mental principles  of  music. 

4.  Music-Feeling,  the  Source  and  Fountain  of  Music 

Where  did  and  does  this  Union  of  Elements  take 
place .?  Within  the  organism,  within  us,  in  feeling. 
Hence,  music-feeling,  the  source  and  fountain  of 
music.  The  harmonic  forms  of  tone  specific  to  music 
had  their  genesis  in  feeling  and  are  the  direct  products 
of  causes  operating  in  feeling.  The  voice  of  music 
is  an  inner  voice,  a  spiritual  voice.  Thus  music 
dwells  within,  proceeds  from  within,  is  understood 
within.  The  germ  or  raw  material  of  musical  sound 
entered  into  feeling  from  without.  But  until  that  germ 
had  been  planted  and  had  taken  firm  root  in  feeling 
it  could  not  develop  and  blossom  into  the  perfect 
tone  or  consonance  upon  the  genesis  of  which  de- 
pended the  genesis  of  music.  Feeling  alone  could, 
did  and  does  transmute  the  raw  material  of  external 
physical  sound  into  the  perfect  harmonic  form  of 
tone  with  which  music  began.  Why  ?  Because  the 
causes  of  this  transmutation  are  psychical  or  spiritual 
causes  which  exist  nowhere  outside  of  feeling,  that  is, 
outside  of  the  mind.  These  causes  explain  why  it  is 
that  every  first  crude  effort  to  intone  rhythm  is  an 


INTRODUCING  FIRST  PRINCIPLES  9 

effort  to  shape  and  express  the  perfect  tone  or  con- 
sonance with  which  music  began;  they  explain  why 
it  is  that  the  perfect  tone  or  consonance  exists  nowhere 
outside  of  feehng,  outside  of  the  mind.  This  is  con- 
clusively proved  by  the  ascertained  fact  that  under 
acoustical  analysis  every  tone  is  a  dissonance.  But 
even  the  form  of  this  acoustical  dissonance  is  not  the 
same  as  that  of  the  original  dissonance  of  music.  That 
and  why  this  is  so  is  explained  by  the  proximate  or 
immediate  cause  of  the  psychogenesis  of  the  specific 
harmonic  forms  of  music.  This  cause  is  relation, 
A  tone's  specific  relation  is  the  immediate  cause  of  its 
specific  harmonic  form.  From  first  to  last  the  origi- 
nal harmonies  of  music,  headed  by  the  perfect  tone 
or  consonance,  arose  one  by  one  in  an  evolutional 
sequence  of  relations  in  obedience  to  an  inherent  shap- 
ing principle.  As  we  proceed  to  trace  the  psycho- 
genesis  of  this  evolutional  sequence  of  correlated  har- 
monies we  shall  obtain  a  view  of  music  in  the  light  of 
its  origin  and  development  and  so  discover  the  nature 
of  our  common  feeling  of  music.  Let  us  be  explicit 
as  to  exactly  what  is  here  meant  hy  feeling  of  music. 
By  music-feeling  I  mean  simply  and  only  the  feeling 
of  music  per  se,  that  is,  the  feeling  of  tone-rhythm, 
that  is,  the  feeling  of  united  rhythm  and  harmony, 
that  is,  the  feeling  of  melody,  the  essence  of  music. 
Here  at  the  outset  let  us  understand  that  this  study  is 
not  concerned  with  an  analysis  of  feeling  in  its  con- 
nection with  any  specific  emotions,  sentiments  and 
associated  ideas  which  are  evoked  by  music.  All 
these  are  most  important  precisely  because  they  are 
purely  personal,  but  their  proper  place  is  in  poetry. 


10  THE  NATURE  OF  MUSIC 

autobiography  and  aesthetics.  In  a  study  like  this  such 
an  analysis  of  personal  experience  would  be  out  of 
place  and  would  lead  us  into  the  cloudland  of  vague- 
ness, mysticism  and  speculation.  Here  let  us  seek  the 
common  truth  in  our  common  experience  of  music. 
We  shall,  however,  consider  certain  fundamental  emo- 
tions, first  because  they  are  common  to  all  of  us  and 
next  because  they  are  inseparable  concomitants  of 
tone-rhythmic  feeling.  The  spirit  and  the  matter  of 
music  are  inseparably  united  as  idea  and  form,  as 
message  and  messenger  of  truth  and  beauty.  The 
tone-rhythmic  messenger  is  the  bearer  of  the  spiritual 
message.  Our  common  knowledge  of  that  message 
is  confined  to  what  can  be  learned  from  the  messenger. 

5.   Cause  of  Union,     Shaping  Principle 

Both  rhythm  and  tone  Sive  forms  of  balanced  motion. 
A  shaping  principle  common  to  both  is  the  cause  of 
their  affinity  and  union.  This  shaping  principle  is 
equilibrium.  Equilibrium  is  harmony.  Harmony  is 
equilibrium.  Tone  -  rhythmic  equilibrium  is  tone- 
rhythmic  harmony.  Tone-rhythmic  harmony  is  tone- 
rhythmic  equilibrium.  The  feeling  of  tone-rhythmic 
equilibrium  or  harmony  is  our  common  feeling  of 
music.  The  feeling  of  tone-rhythm  and  its  shaping 
principle,  while  it  explains  why  every  initial  effort  to 
intone  rhythm  is  an  effort  to  shape  and  express  the 
perfect  harmonic  form  of  tone  essential  to  the  genesis 
of  music,  it  does  not  explain  why  that  effort  is  made, 
that  is,  it  does  not  explain  the  cause  which  gave 
and  gives  the  impulse  to  that  effort.  What  is  this 
impelling  cause.?     It  is  a  spiritual  cause,  a  common 


INTRODUCING  FIRST  PRINCIPLES  11 

emotion,  an  inseparable  concomitant  of  tone-rhythmic 
feeling,  namely,  the  innate  desire  to  shape  and  ex- 
press with  no  other  end  and  aim  than  the  pleasure  of 
gratifying  that  desire.  This  impelling  desire  of  the 
inner  life  or  human  spirit  to  give  form  to  its  moods 
and  tenses  for  pure  joy  and  love  of  expression  is  the 
creative  impulse  to  which  all  the  arts  owe  their  rise 
and  development.  Goethe's  dictum  "art  is  but 
form"  is  comprehensive,  since  form  in  art  is  the 
direct  product  of  the  human  spirit  and  is  not  separa- 
ble from  the  idea  which  it  embodies.  Equilibrium  or 
harmony  is  the  shaping  principle  of  all  form  of  mo- 
tion, of  all  physical /orm  of  expression,  of  all  spiritual 
form  of  expression.  We  are  here  confronted  by  a 
world-principle,  a  principle  inherent  in  the  physical 
and  psychical  forces,  a  principle  governing  all  animate 
and  inanimate  form  of  cosmic  expression.  This  uni- 
versal principle  of  harmony  and  the  principle  of  har- 
mony in  music  are  one  and  the  same.  This  princi- 
ple is  the  ejSicient  cause  of  the  genesis  in  feeling  of  the 
original  forms  of  harmony,  the  evolutional  anteced- 
ents of  chords. 

6.    World-Energy 

World-energy  is  manifested  in  motion.  Its  mani- 
festations may  be  summarily  divided  as  follows: 
First,  motion  in  process.  Second,  record  of  previous 
motion  or  process.  The  first  includes  all  sensible 
motion  within  and  about  us.  The  second  includes 
all  the  forms  or  works  of  nature  and  all  the  works  of 
man.  All  motion  is  accentual,  wherefore  all  process 
and  record  of  motion  are  accentual. 


n  THE  NATURE  OF  MUSIC 

7.    World-Rhythm.     Universal  Form 

World-motion  is  accentuated  motion,  in  one  word, 
is  rhythm.  Rhythm  is  form  not  law  of  motion.  Let 
us  not  confound  form,  which  is  rhythm,  with  the 
principle  or  cause  of  form,  which  is  inherent  in 
and  proceeds  from  energy  itself.  World-energy  is 
manifested  in  world-rhythm.  Hence  this  principle. 
Rhythm  is  the  universal  form  of  expression.  At  bot- 
tom, the  terms  expression,  manifestation,  language, 
are  synonymous.  Not  man  alone  speaks.  All  things 
speak,  each  in  its  own  peculiar  language,  but  all  in 
common  rhythmic  accents  in  time  and  space.  Vibra- 
tion, pulsation,  undulation,  are  so  many  names  for 
accentuated  motion,  that  is,  for  regularly  recurring 
periods  of  rhythm. 

8.    World-Harmony.     Universal  Principle  of  Form 
and  Relation 

World-rhythm  everywhere  makes  for  world-har- 
mony, world-equilibrium.  World-energy  persists  in 
its, perpetual  rhythmic  struggle  for  the  maintenance 
of  world-harmony,  world-equilibrium.  Hence  this 
all-pervading,  all-shaping,  all-governing  principle. 
Harmony  (equilibrium)  is  the  universal  principle  of 
form  and  relation  in  time  and  space.  The  universe 
is  one  rhythm  proceeding  from  one  energy  and 
maintaining  one  equilibrium  to  which  the  rhythm 
and  equilibrium  of  all  its  parts  from  greatest  to 
smallest  are  relative.  Hence  the  harmony  and 
unity  of  the  universal  whole,  the  interdependence  and 
interrelation  of  all  things,  the  reign  of  law  and  order 


INTRODUCING  FIRST  PRINCIPLES  13 

in  time  and  space.  In  this  connection,  harmony, 
equihbrium,  balance,  unity,  are  interchangeable 
terms.  The  ceaseless  rhythmic  struggle  and  ''stream 
of  tendency"  within  us  and  all  about  us  ceaselessly 
makes  for  harmony.  This  rhythmic  struggle  and 
its  governing  principle  are  manifested  throughout 
inorganic  and  organic  nature  in  every  movement  and 
every  form  or  record  of  movement.  Harmony 
(equilibrium)  is  a  fundamental  principle  of  evolu- 
tion. In  fulfilment  of  this  inner  principle  of  "  being 
and  becoming,"  all  things  pass  through  rhythmic 
stages  of  progression  and  resolution,  that  is,  rhythmic 
stages  of  evolution.  Life  from  moment  to  moment  ' 
is  a  rhythmic  struggle  for  equilibrium.  The  works 
of  man  are  records  of  his  physical,  mental,  moral 
and  spiritual  struggle  for  equilibrium.  In  his  music- 
works  man  has  recorded  and  will  continue  to  record 
the  essence  of  his  universal  and  spiritual  experience 
in  his  only  universal  and  purely  spiritual  language, 
music.  The  realm  of  music,  the  tone-realm,  is  an 
evolutional  product  of  the  inner  life  or  spirit;  it 
is  the  spiritual  counterpart  and  image  of  the  uni- 
versal whole,  of  its  perfect  law  and  order  in  time  and 
space.  Music  is  the  concrete  language  of  universal 
harmony,  law  and  order.  Music-feeling  is  univer- 
sal feeling,  that  is,  the  concrete  feeling  of  universal 
harmony,  law  and  order.  I  emphasize  concrete 
because  all  that  is  music  and  music-feeling  is  con- 
crete reality,  a  concrete  and  vivid  inner  experience,  a 
common  experience  in  all  of  us.  In  music,  rhythm 
is  form,  relation,  law  and  order  in  time;  tone 
(harmony  of  sound)  is  form,  relation,  law  and  order 


14  THE  NATURE  OF  MUSIC 

in  space;  the  tone-rhythmic  embryo  or  composite 
of  the  two  unites  pure  time-form  and  pure  space- 
form,  pure  time-relation  and  pure  space-relation; 
this  composite,  as  we  shall  demonstrate,  is  melody, 
the  essence  of  music,  the  free  spirit  of  the  free  tone- 
realm.  Melody  makes  for  pure  and  perfect  har- 
mony in  time  and  space  and  thus  fulfils  the  inner 
law  and  purpose  of  its  being.  In  our  common  feel- 
ing of  melody  we  shall  discover  the  identity  of 
harmony  and  equilibrium.  As  we  proceed  to  trace 
the  evolution  of  tone-rhythm  we  shall  observe  the 
operation  of  this  universal  principle  in  the  domain 
of  the  mind.  Harmony  (equilibrium)  is  the  govern- 
ing principle,  the  will  of  the  material  and  spiritual 
universe.  In  the  human  spirit  this  principle  mani- 
fests itself  in  a  common  emotion,  in  a  common  desire 
for  and  love  of  harmony,  to  gratify  which  is  to  be 
led  by,  to  follow,  to  obey,  the  universal  will.  This 
spiritual  desire  and  love  discovered  its  voice  in 
melody,  rhythm  was  intoned;  the  heart  thus  found 
a  perfect  vehicle  for  all  its  moods  and  tenses.  Hence 
music,  its  genesis,  its  raison  d'etre^  its  function,  its 
messenger,  its  message.  Thus  music  and  its  forma- 
tive principle  are  deeply  rooted  in  what  Goethe 
calls  "eternal  things"  and  "the  great  whole;" 
its  composite  rhythmo-harmonic  relations  are  what 
that  poet-evolutionist  calls  "abiding  relations."  In 
the  light  of  the  principle  of  world-harmony  I  under- 
stand Schopenhauer's  definition  of  music,  "  das  innere 
Bildder  Welt." 


INTRODUCING  FIRST  PRINCIPLES  15 

9.    Cardinal  Principle 

Harmony  (equilibrium)  as  just  defined  is  the 
cardinal  principle  responsible  for  the  genesis  and 
evolution  of  music  and  music-feeling,  for  all  that  is 
law,  order,  form,  relation,  proportion  and  structure 
in  music.  Thus  all  the  principles  and  laws  of 
music,  of  its  elementary  forms  and  their  original 
relations  and  of  the  gradual  expansion  of  its  forms 
and  relations,  are  so  many  different  manifestations 
of  the  operation  of  this  one  all-shaping  and  all- 
explaining  principle.  Under  the  impulse  of  princi- 
ples and  laws  operating  in  feeling  music  sprang  into 
being  and,  passing  through  a  series  of  natural  and 
interdependent  stages,  evolved  from  simple  to  more 
and  more  complex  forms,  from  a  state  of  nature  to 
an  art.  Nature-music  and  art-music  differ  only  in 
degree,  not  in  kind;  the  same  fundamental  prin- 
ciples and  laws  underlie  both. 

10.    One  Music 

Nature-music  includes  the  songs  of  birds  and  all 
those  human  melodies  of  the  homophonic  period  in 
the  production  of  which  man  was  guided  wholly  by 
intuition  and  the  impulses  of  the  heart  and  simply 
obeyed  his  innate  feeling  of  the  principles  and  laws 
of  tone-rhythm.  This  intuitional  evolution  of  nature- 
music  reached  its  culmination  in  that  lovely  and  per- 
fect flower,  the  folksong.  Nature  had  spent  incal- 
culable ages  in  the  production  of  this  perfect  form 
of  melody,  had  thus  fulfilled  her  mission  and  laid 
the  foundation  for  the  art  of  pure  music.     From  the 


16  THE  NATURE  OF  MUSIC 

simplest  homophonic  motive  and  phrase  to  the 
perfect  symmetry  of  the  folksong  this  nature-music 
is  the  pure  music  of  intuition  and  the  heart,  the  pure 
expression  of  concrete  music-feeling.  Nature  had 
not  only  produced  the  germs  which  were  destined 
to  develop  into  the  great  art  of  pure  music  but 
had  chosen,  followed,  prepared  and  pointed  out  the 
true  path  for  the  development  of  this  art.  This 
path  of  intuition  and  concrete  music-feeling  was 
chosen  and  followed  by  the  only  art  of  pure  music 
which  the  world  has  produced.  This  pure  art  is 
modern  music  which  is  distinctively  the  product  of 
Western  civilization  and  the  only  music-art  directly 
connected  with  and  based  on  nature-music.  Hence 
one  music,  one  continuous  evolution  from  the  earliest 
beginnings  of  nature-music  to  the  art  of  the  present 
time.  This  one  music  is  the  only  music  which 
concerns  us  in  these  pages.  Whatever  else  may  be 
said  of  the  manifold  theories  to  which  the  modern 
art  of  music  has  given  rise,  one  thing  is  true  of  all, 
namely,  all  seek  to  explain  and  conform  with  the 
nature  and  testimony  of  intuitive  music-feeling  in 
their  common  endeavor  to  discover  and  present  the 
true  principles  and  laws  of  the  art  of  music.  Man 
has  produced  other  species  of  music-art  whose 
forms  and  theories  are  not  based  on  intuition  and 
concrete  feeling.  An  extinct  art  of  this  species  is 
that  of  ancient  Greece.  An  extant  art  of  this  species 
is  that  of  China.  Yet  when  we  consider  the  beauti- 
ful tributes  paid  to  music  by  Homer  and  Confucius 
we  are  led  to  infer  that  these  two  unmusical  arts 
had    been    preceded    by   an    evolutional    period    of 


INTRODUCING  FIRST  PRINCIPLES  17 

nature-music  when  both  Greek  and  Chinaman  were 
guided  by  intuition  and  the  heart,  when  Hke  the 
birds  they  freely  sang  just  as  they  happened  to  feel. 
Why  in  those  two  eases  the  natural  attitude  toward 
music  was  forsaken  in  favor  of  arbitrary  theories  is 
a  question  closely  connected  with  the  life  and  spirit 
of  the  two  nations,  a  discussion  of  which  does  not 
enter  into  the  plan  of  this  book.  Our  subject  has 
been  defined,  it  is  one  music,  in  the  nature-stages  of 
which  human  selection  was  unconsciously  governed 
by  natural  selection,  in  the  art-stages  of  which  human 
selection  was  consciously  governed  by  natural  selec- 
tion. 

11.   Rationale  of  Micsic 

The  elemental  what  of  music  is  form  and  relation 
of  united  rhythm  and  tone.  The  explanation  of 
this  form  and  relation,  their  inherent  principles  and 
laws,  will  discover  not  alone  the  true  nature  of 
this  elemental  what,  but  also  answers  to  its  how? 
and  why?  Elemental  tone-rhythm  and  its  indwell- 
ing principles  and  laws  of  self-development  there- 
fore constitute  the  what,  how  and  why,  in  a  word, 
the  rationale  of  music.  What.?  is  the  question  of 
ultimate  importance.  Until  this  essential  question 
is  answered  the  inquiries  how.?  and  why.?  are  futile 
since  they  lack  a  subject,  since,  in  other  words,  we 
do  not  know  what  we  are  inquiring  about. 

12.    Common  Reports  of  Commxm  Feeling 

Whether  their  theories  are  based  on  acoustics, 
physiology  or  psychology,  all  investigators  set  out 
with  a  common  view  of  the  ultimate  question  What 


18  THE  NATURE  OF  MUSIC 

is  music?  a  question  so  often  set  aside  as  an  insol- 
uble mystery.  This  common  view  of  theorists  is 
shown  in  three  significant  essentials  the  importance 
of  which  is  greater  than  at  first  appears. 

First:  Admittedly  or  tacitly  all  premise  that  music 
is  what  we  hear  it  to  be  and  thus  transmute  the 
form  of  the  ultimate  question  What  is  music  .^  into 
What  do  we  hear  music  to  be  ?  or  briefly,  What  do 
we  hear.?  That  music  is  what  we  hear  is  not  a 
remarkable  observation  for  what  else  could  it  he? 
However,  the  question  What  do  we  hear.?  really 
means  What  do  we  all  hear  in  common.?  and  this 
question  no  one  has  as  yet  succeeded  in  answering. 

Second:  At  the  outset  all  agree  that  what  we  hear 
is  consonance  and  dissonance.  This  again  trans- 
mutes the  form  of  the  ultimate  question  into  What 
is  consonance  and  what  is  dissonance .?  A  scientifi- 
cally verified  answer  to  this  question  has  not  yet 
appeared  in  the  books,  and  there  are  those  who 
believe  that  this  answer  cannot  be  discovered  in  the 
three  sciences  mentioned  above,  wherefore  it  should 
be  sought  elsewhere.* 

Third:  All  acknowledge  the  existence  of  such  a 
thing  as  common  music-feeling  to  which  the  appeal 
is  general  whenever  and  wherever  laws  and  rules 
either  fail  to  apply  or  cannot  be  found.  This  gen- 
eral appeal  to  music-feeling  is  equivalent  to  a  general 
belief  in  its  essential  validity,  a  general  belief  that 
in  it  the  ultimate  and  whole  truth  of  music  lies 
dormant,  a  general  belief  that  the  feeling  is  common 
to  all.  If  there  is  such  a  thing  as  common  music- 
feeling,  then  there  are  such  things  as  common  music- 


INTRODUCING  FIRST  PRINCIPLES  19 

perception,  as  common  reports  of  common  feeling 
verifiable  by  common  observation.  What  are  these 
common  reports  and  their  immutable  principle? 
This  question  has  not  yet  been  answered.  The 
answer  to  this  question  would  discover  the  true 
basis  of  music  and  its  science,  it  would  be  the  initial 
step  toward  a  common  conception  of  the  ultimate 
what  of  music,  it  would  eventually  result  in  a  com- 
mon recognition  and  adoption  of  the  one  true  basis. 

In  these  pages  it  is  my  purpose  to  show  that  such 
things  as  common  reports  verifiable  by  common 
perception  do  exist  and  may  be  clearly  presented 
and  explained.  The  ultimate  question  What  is 
music .^  now  assumes  the  following  form:  What  are 
the  common  reports  of  common  feeling  and  per- 
ception of  consonance  and  dissonance,  their  inher- 
ent principles  and  laws.^  It  is  clear  that  this  is  a 
psychological  question,  a  question  addressed  to  the 
inner  ear  of  the  mind,  a  question  of  psychological 
acoustics,  not  of  physical  acoustics.  Though  this 
question  places  the  present  writing  upon  an  inde- 
pendent basis  and  defines  the  writer's  position, 
the  psychology  of  this  position  still  requires  some 
explanation. 

We  are  told  by  M.  Hauptmann  *  that  it  is  custom- 
ary to  begin  a  treatise  on  harmony  with  a  learned 
chapter  on  acoustics  the  half-truths  in  which,  how- 
ever, have  little  if  any  influence  upon  and  are  often 
not  again  referred  to  in  the  subsequent  chapters  of 
the  book.  Acoustics  treats  the  question  What  do  we 
hear?  on  its  physical  side  and  therefore  objectively, 
as  every  one  knows.     Music  as  we  hear  it  does  not 


20  THE  NATURE  OF  MUSIC 

exist  objectively,  as  we  shall  see.  The  acoustic 
series,  consisting  of  fundamental  and  overtones, 
teaches  us  that  every  tone  is  a  dissonance  and  proves 
this  to  be  a  fact,  and  thus  at  the  outset  music  and 
acoustics  are  irreconcilable  antagonists.  But  this 
physical  tone  is  not  a  dissonance  in  the  specific 
musical  sense  of  the  term ;  it  is  in  truth  a  discord,  and 
discords  have  nothing  to  do  with  music.  Although 
it  is  the  custom  in  music-treatises  to  present  only  the 
first  six  tones  of  the  acoustic  series,  yet  this  arbitrary 
omission  of  the  remaining  objectionable  because  dis- 
cordant overtones  does  not  eliminate  them,  they  are 
there  just  the  same,  and  are  met  as  they  should  be 
by  physical  science.  Whatever  be  their  pitch  all 
tones  have  the  same  internal  physical  formation, 
therefore  all  tones  are  discords.  If  one  tone  is  a 
discord  what  a  blood-curdling  horror  such  an  amor- 
phous physical  composite  as  the  chord  ought  to  be! 
But  common  music-feeling  and  perception  reject 
all  this  as  false.  If  we  really  heard  tones  in  their 
actual  physical  forms  all  hands  would  be  raised  to 
stop  the  ears.  Notwithstanding  all  this  most  of  our 
music-theories  are  based  on  physical  acoustics;  a 
scientific  basis  for  music  being  required,  and  no 
other  being  at  hand  we  seize  upon  physics  for  an 
initial  chapter.  Music's  pure  and  perfect  conso- 
nance, music's  specific  form  and  relation  of  tone, 
these  things  do  not  exist  objectively,  they  are  sub- 
jective products  of  psychological  development,  direct 
products  of  music-feeling,  which  is  the  feeling  of 
composite  rhythm  and  harmony.  Roughly  stated, 
elemental    tone-rhythmic    feeling    impelled    by    an 


INTRODUCING  FIRST  PRINCIPLES  21 

inherent  immutable  principle,  equilibrium,  has  re- 
solved objective  physical  sound  or  discord  into  sub- 
jective harmony. 

The  rejection  by  music-feeling  and  perception  of 
physical  acoustics  as  a  basis  directly  points  to  psy- 
chology for  the  solution  of  music's  ultimate  problems 
and  the  discovery  of  music's  cardinal  principle. 
Though  the  conviction  that  there  is  such  a  princi- 
ple has  often  been  expressed  the  psychologist  has 
thus  far  been  unable  to  explain  what  it  is;  he  has 
left  the  true  nature  of  common  music-feeling  shrouded 
in  mystery  and,  like  the  physicist  and  physiologist, 
has  left  the  problem  of  consonance  and  dissonance 
unsolved.  The  psychologist  has  followed  one  of 
two  courses:  either  he  has  made  a  comparative 
study  of  music  and  music-feeling  in  the  light  of  the 
data  of  physics  and  physiology,  like  C.  Stumpf,  or 
he  has  delved  more  or  less  deeply  into  metaphysical 
speculations  and  aesthetics.  The  physiologist  deals 
with  the  physical  organ  of  hearing  and  its  function, 
and  in  his  hands  the  question  What  do  we  hear? 
assumes  the  form  How  do  we  hear.?  which  is  a 
subordinate  question  that  predicates  a  knowledge 
of  music's  ultimate  what  When  psychology  has 
once  answered  the  ultimate  question,  then  only  will 
physics  and  physiology  gain  a  legitimate  subject 
for  musical  research  the  importance  and  value  of 
which  to  music  can  alone  be  estimated  in  the 
future. 

The  writer's  position  thus  roughly  sketched  may  be 
summed  up  as  follows:  The  true  nature  of  music 
per  se,  of  its  specific  forms   and   relations,   of   its 


■22  THE  NATURE  OF  MUSIC 

inherent  principles  and  laws,  are  problems  of  psy- 
chology the  solution  of  which  can  alone  be  found  in 
what  I  have  called  the  common  reports  of  common 
feeling  verifiable  by  common  perception. 

13.   Elemental  Form 

Form  is  vehicle  or  messenger,  not  message,  but 
bearer  of  message.  We  are  here  primarily  concerned 
with  the  messenger,  not  with  the  message  of  music, 
since  all  that  can  be  learned  of  the  latter  depends  upon 
what  can  be  learned  of  the  former.  The  two  should 
not  be  confounded.  Elemental  form  or  messenger 
of  music  is  united  rhythm  and  tone.  In  this  elemen- 
tal form  lies  music's  elemental  truth  and  beauty, 
the  study  of  which  involves  neither  vagueness  nor 
speculation  and  alone  concerns  us  in  these  pages. 
Vague,  mysterious,  inscrutable,  yet  none  the  less 
real  and  important  is  the  spiritual  message  of  music, 
a  message  of  universal  harmony  and  unity.  How- 
ever, the  spiritual  message  of  truth  and  beauty,  the 
emotions,  poetic  and  religious  sentiments  and  the 
aesthetic  and  metaphysical  speculations  and  theories 
to  which  it  gives  rise,  belong  not  to  music  alone,  but 
to  all  the  arts  and  to  all  things.  By  the  word  feeling 
in  connection  with  music  I  mean  simply  and  only 
feeling  of  united  rhythm  and  tone,  which  is  music- 
feeling  per  se  and  common  to  all  of  us. 

14.   Elemental  Relation 

A  tone's  relation  in  time  is  its  rhythmic  relation. 
JA  tone's  relation  in  space  is  its  harmonic  relation. 
Thus  tone-relation  is  a  composite  of  time-relation 


INTRODUCING  FIRST  PRINCIPLES  23 

and  space-relation,  in  one  word,  is  a  rhythmo-har- 
monic  relation.  Every  tone  in  music  is  heard,  felt, 
thought,  expressed  and  recorded  in  such  a  com- 
posite relation,  every  tone-moment  is  a  rhythmo- 
harmonic  moment.  It  is  true  that  in  analysis  we 
seem  to  separate  this  composite,  now  observing  the 
rhythmic  form  and  relation  and  now  the  harmonic 
form  and  relation,  yet  we  do  not  and  cannot  fully 
comprehend  the  one  apart  from  its  relation  to  the 
other.  The  word  harmony  in  its  specific  musical 
sense  means  harmony  of  sound,  which  is  tone.  In 
this  sense  one  tone,  every  tone  is  a  harmony,  as  will 
be  explained  in  the  next  paragraph. 

15.   Melody y  a  Composite,  not  an  Element 

Nothing  could  be  more  untrue  than  the  time- 
honored  teaching  and  belief  that  melody,  harmony 
and  rhythm  are  the  three  elements  of  music.  Music 
has  two,  not  three  elements.  Rhythm  is  an  element. 
Harmony  (tone)  is  an  element.  Melody  is  not  an 
element.  Melody  is  a  composite  of  music's  two 
elements,  rhythm  and  harmony  (tone).  It  is  impos- 
sible to  conceive  of  melody  either  without  rhythm 
or  without  harmony  (tone).  Hence  the  obvious  truth 
that  melody  is  a  composite  and  not  an  element. 
Everything  from  a  motive  in  two  tones  onward, 
whether  it  issues  from  the  throat  of  a  bird  or  was 
penned  by  a  classic  composer,  is  a  melody,  a  com- 
posite of  rhythm  and  harmony  (tone).  Melody  is 
the  essence  of  a  music-idea  or  thought.  Melody  is 
the  original  and  essential  vehicle  of  music.  Melody 
is  the  original,  universal  and  sovereign  voice  and 


24  THE  NATURE  OF  MUSIC 

genius  of  music.  Conversely,  music  ever  has  been, 
is,  and  ever  will  be  melody.  Melody  is  the  raison 
d'etre  of  music's  harmony.  Why  this  rhythm  ?  Why 
that  harmony  ?  The  answers  to  these  questions  lie  in 
melody.  Love  of  music  and  love  of  melody  are  one. 
No  melody,  no  music-idea  or  thought.  No  melody, 
no  harmony.  No  melody,  no  music.  The  great 
and  greatest  in  music  are  its  melodies;  types  in 
music  are  types  of  melody  and  from  first  to  last 
music's   great   masters   are   melodists. 

The  above  conclusions  are  verified  by  common 
report  of  common  feeling  and  perception  of  original 
harmony  in  one  voice.  In  a  book^  published  in 
1890,  the  writer  introduced  the  subject  of  harmony 
in  one  voice  naming  it  meloharmony^  the  inherent 
harmony  of  melody. 

16.    The  Efficient  Accent  and  Regnant  Harmony 

In  a  preceding  paragraph  it  was  stated  that  the 
principles  and  laws  of  music  are  rooted  in  the  cardinal 
shaping  principle,  equilibrium.  The  rhythmo-har- 
monic  forms  and  relations  of  music  in  one  voice  or 
homophonic  melody  discover  the  nature  and  oper- 
ation of  two  evolutionary  principles  which  next 
require  provisional  introduction  and  explanation. 
First  and  most  important  of  the  two  is  the  efficient 
accent  which  is  the  efiicient  cause  of  the  genesis  of 
tones  and  tone-relations,  that  is,  of  music's  specific 
and  basic  harmonies. 

The  eflScient  accent  is  the  heavy  'periodic  accent  oj 
rhythm^  it  is  the  harmony-generating  and  harmony- 

*  Th£  Septonate  and  the  Centralization  of  the  Tonal  System. 


INTRODUCING  FIRST  PRINCIPLES  25 

maintaining  accent  of  music.  Under  the  name 
rhythmo-harmonic  accent  or  point,  I  presented  this 
subject  fourteen  years  ago  in  the  book  above  alluded  to. 

In  one-voice  music,  not  only  is  each  tone  in  a 
melody  a  harmonic,  that  is,  a  root  or  third  or  fifth  or 
seventh  or  ninth,  but  every  moment  in  a  melody 
is  ruled  by  a  particular  harmony  which  I  call  the 
regnant  harmony.^ 

In  one  voice  the  regnant  harmony  arises  on  the 
line  of  least  resistance,  it  elects  and  asserts  itself, 
it  is  generated  in  feeling  by  the  efficient  accent,  it 
determines  and  reports  the  exact  harmonic  form 
and  relation  of  each  tone;  these  forms  and  rela- 
tions are  immutable,  since  in  every  given  case  we 
all  of  us  hear  and  perceive  the  same  form  and  same 
relation. 

We  shall  see  that  the  original  harmonies  entered 
into  being  one  by  one  as  integral  and  correlated 
threads  of  an  ever  increasing  web  of  forms  and 
relations  in  an  orderly  sequence  of  regnant  har- 
monies, a  sequence  which  nolens  volens  repeats  itself 
in  the  development  of  every  musical  mind,  thus 
establishing  a  traceable  psychological  connection  be- 
tween music's  present  and  past.  We  cannot  study 
and  trace  this  evolutionary  sequence  and  psycho- 
logical development  in  multi-voice  music  for  the 
simple  and  obvious  reason  that  in  such  music  the 
regnant  harmonies  are  due  to  personal  election,  fancy 
and  taste.  In  one  voice  the  regnant  harmony  elects 
itself,  while  in  more  than  one  voice  the  choice  of  har- 
monies is  personal.  In  one  voice  we  perforce  agree, 
while  in  several  voices  we  are  at  liberty  to  disagree. 


26  THE  NATURE  OF  MUSIC 

17.   Principle  of  Potential  Harmony 

The  next  evolutionary  principle  to  be  introduced 
is  that  of  potential  harmony,  which  I  define  as  fol- 
lows: Every  harmonic  relation  in  experience  is  poten- 
tial in  every  tone  in  experience.  Thus  all  harmonic 
relations  are  potential  in  all  tones.  In  other  words, 
any  harmonic  relation  may  be  duplicated  on  any 
tone.     Let  us  explain. 

There  are  original  tones,  original  harmonic  forms, 
original  harmonic  relations.  The  seven  tones  of  the 
major  scale  constitute  the  first  group  of  original 
tones.  Certain  of  these  tones  first  arose  in  the 
harmonic  form  of  consonance,  certain  others  in  that 
of  dissonance.  This  specific  consonance  and  this 
specific  dissonance  are  therefore  the  original  har- 
monic forms.  Again,  each  of  these  seven  originals 
first  arose  in  a  certain  definite  harmonic  relation  as 
a  root  or  third  or  fifth  or  seventh  or  ninth.  The 
original  relation  of  a  tone  is  therefore  the  relation  in 
which  a  tone  first  arose.  Everything  is  and  has 
been  derived  from  relation;  harmonic  form  and 
harmonic  relation  are  connate;  the  former  is  due  to 
the  latter,  the  former  changes  when  the  latter  changes. 
Since  each  original  tone  entered  into  being  in  a  cer- 
tain original  relation,  the  fundamental  importance 
of  relation  is  manifest. 

In  the  psychological  process  of  development  each 
tone  and  relation  entered  into  experience  first  as  a 
mere  feeling,  it  remained  latent  in  feeling  until  it  was 
seized  upon  by  consciousness  when  it  became  a  per- 
cept,  and  last  of  all  it   became   a   concept.      The 


INTRODUCING  FIRST  PRINCIPLES  27 

harmonic  idea  of  music  is  therefore  a  complex  of  har- 
monic percepts,  each  of  which  is  either  an  original 
harmonic  relation,  or  has  been  derived  from  an  origi- 
nal relation.  How  derived?  Through,  the  evolu- 
tionary principle  of  potential  harmony  in  cooperation 
with  the  efficient  accent,  the  principle  of  harmonic 
genesis,  roughly  as  follows:  Each  toners  original  rela- 
tion is  duplicated  on  other  tones.  For  example:  the 
tone  known  as  the  Tonic  (also  called  keynote)  first 
arose  as  a  root  and  eventually  appeared  as  third, 
fifth,  seventh  and  ninth,  thus  duplicating  the  origi- 
nal relations  of  other  tones.  Like  duplications  were 
in  time  effected  on  other  original  tones  which  had 
their  genesis  in  other  relations.  We  shall  see  that 
these  duplications  are  responsible  for  the  genesis  of 
new  tones  and  new  harmonic  relations  thus  opening 
the  way  to  new  duplications,  and  we  shall  see  that  the 
expansion  of  harmonic  relations  and  of  the  tone-sys- 
tem is  the  direct  product  of  this  psychological  process, 
in  short,  that  harmonic  relation  and  our  tone-system 
are  inseparably  linked  in  their  development  as  cause 
and  consequence.  But  how  did  the  seven  original 
tones  arise  ?  How  did  the  first  consonance  and  first 
dissonance  arise  .^  Unless  these  origins  can  be  ex- 
plained the  principle  of  potential  harmony  has  no 
material  to  develop,  no  valid  basis  to  rest  on,  is 
but  an  empty  phrase.  The  above  questions  will  be 
answered  in  the  two  subsequent  chapters. 

18.   Basis  of  Verification 

A  brief  summary  of  the  position  outlined  in  the 
preceding  paragraphs  will  lead  the  way  to  a  simple 


28  THE  NATURE  OF  MUSIC 

explanation  of  how  the  test  of  truth  is  to  be  applied 
in  the  subsequent  study  and  analysis  of  music.  The 
essential  points  are  as  follows :  — 

The  "being  and  becoming"  of  music  are  due  to  the 
union  in  feeling  of  rhythm  and  tone. 

Form  and  relation  are  form  and  relation  of  united 
rhythm  and  tone. 

All  tones  are  harmonic.  Original  harmony  is  har- 
mony in  one  voice;  it  asserts  itself  and  is  latent  in 
common  music-feeling,  therefore  in  all  of  us.  Har- 
mony in  one  voice  reports  the  same  relations  in  all 
of  us. 

Melody  is  the  composite  of  the  two  elements, 
rhythm  and  harmony  (tone);  it  is  the  original  and 
universal  voice  of  music. 

Common  music-feeling  is  united  rhythm-feeling  and 
tone-feeling. 

One  music,  one  basis  of  music,  one  common  music- 
feeling,  one  all-shaping  principle  in  which  all  princi- 
ples and  laws  are  rooted.  This  cardinal  principle 
is  equilibrium,  is  common  to  and  inherent  in  both 
rhythm  and  tone,  and  is  the  cause  of  their  union,  and 
it  dwells  and  operates  in  common  feeling  in  all  of  us. 

All  who  take  any  degree  of  pleasure  in  music  are 
musical  and  share  in  the  common  feeling.  All  such 
may  by  guidance  and  study  transmute  latent  feeling 
of  united  rhythm  and  tone  into  definite  observation, 
intelligent  appreciation,  understanding. 

Community  of  feeling  leads  to  community  of  per- 
ception and  thence  to  community  of  conception.  All 
may  learn  the  common  reports  of  common  feeling  and 
verify  such  reports  by  personal  observation. 


INTRODUCING  FIRST  PRINCIPLES  29 

The  test  of  truth  here  indicated  is  the  simplest. 
What  all  perceive  or  observe  in  common  is  the  truth. 
Truth  is  the  correspondence  of  an  expressed  idea  with 
common  experience.  The  truth  of  music  Hes  in 
music  itself,  in  music  stripped  of  all  associated  ideas 
and  sentiments;  it  lies  in  tone-rhythm,  and  in  tone- 
rhythm  we  will  seek  it.  Two  simple  examples  will 
illustrate  our  test  of  truth. 

1.  Whether  we  know  it  or  not  we  all  feel  and  ex- 
press a  dual  rhythm  in  dual  periods,  a  triple  rhythm 
in  triple  periods.  Hundreds  and  thousands  sing,  beat 
time  and  march  to  the  music  of  a  national  air  in  com- 
plete ignorance  of  the  rhythm  which  they  feel  and 
express  in  common.  However,  the  moment  we  learn 
to  observe  a  dual  rhythm  by  its  dual  periods  and  a 
triple  rhythm  by  its  triple  periods,  we  all  acquire  the 
same  knowledge  in  the  same  way,  namely,  by  trans- 
muting a  common  feeling  into  a  common  perception 
or  observation. 

2.  Whether  we  know  it  or  not  we  all  feel  and  ex- 
press tones  as  roots,  thirds,  fifths,  sevenths  and  ninths, 
some  in  cadence,  some  in  repose.  The  same  hun- 
dreds and  thousands  feel  and  express  these  harmonic 
relations  of  tones  with  the  same  complete  ignorance 
of  what  they  are.  When  these  harmonic  relations  are 
learned  they  are  learned  in  the  same  way,  namely,  by 
transmuting  common  feeling  into  common  observa- 
tion. 


CHAPTER   II 

RHYTHM  AND  TONE 

19.   Definitions 

Rhythm  is  balanced  motion.  Tone  is  balanced 
sound. 

Rhythm  is  order,  form  and  relation  in  time.  Tone 
is  order,  form  and  relation  in  space  (pitch). 

Rhythm  is  harmony  (equilibrium)  in  time.  Tone 
is  harmony  (equilibrium)  in  space  (pitch). 

United  rhythm  and  tone  is  united  order,  form,  rela- 
tion and  harmony  in  time  and  space. 

The  elemental  forms  and  relations  of  rhythm 
which  underlie  all  music-rhythms  are  not  specific  to 
music,  they  exist  everywhere. 

The  elemental  harmonic  forms  and  relations  of 
tone  which  underlie  all  harmonic  forms  and  rela- 
tions of  music  are  specific  to  music,  they  exist  in 
music  alone. 

Numbers  are  symbols  of  order  and  relation.  The 
numbers  2  and  3,  their  multiples  and  combinations 
are  the  symbols  of  rhythmic  order  and  relation  of 
tones,  of  order  and  relation  in  time.  The  numbers 
1,  3,  5,  7,  9  which  indicate  a  root  or  fundamental, 
its  third,  fifth,  seventh  and  ninth  are  the  symbols  of 
harmonic  order  and  relation  of  tones,  of  order  and 
relation  in  space  (pitch). 


RHYTHM  AND  TONE  31 

20.  Analysis  of  Rhythm 
Rhythmic  balance  is  generated  and  maintained  by 
regularly  recurring  accents.  Common  rhythmic  feel- 
ing impels  us  to  follow  up  an  initial  group  of  two 
pulses  by  another,  two  such  groups  by  two  more,  and 
so  on.  Likewise  we  are  impelled  to  follow  up  an 
initial  group  of  three  pulses  by  another,  two  such 
groups  by  two  more,  and  so  on.    Examples  are  given : 

1.    TWO-PULSE  RHYTHMS 


2.    THREE-PULSE  RHYTHMS 

etc 


*)C    1_L/TIL/^LJL^    rr^ 


')L.C_r  ^CQ  CLI  CD 


etc. 


Our  spontaneous  desire  to  arrange  pulses  in  regular 
accentual  groups,  and  to  repeat  and  develop  an  initial 
group,  is  no  more  nor  less  than  the  natural  desire  to 
keep  balance,  to  keep  time,  to  obey  the  inherent  and 
innate  shaping  principle,  equilibrium.  To  keep 
time  is  to  keep  balance,  to  keep  balance  is  to  keep 
time. 


32  THE  NATURE  OF  MUSIC 

In  the  above  examples  each  pulse,  each  group  of 
pulses,  each  combination  of  groups,  is  a  period  of 
rhythm.  Henceforth  in  these  pages  the  term  period 
will  be  employed  exclusively  in  this  connection  with 
rhythm.  Rhythm-periods  are  balanced  h'm^-periods. 
Rhythmic  accents  are  balance-generating  and  balance- 
maintaining  time-accents.  A  period  of  time  is  a 
rhythmic  moment,  a  time-accent  is  an  accentual 
moment  in  feeling  and  consciousness.  Under  the  sway 
of  innate  rhythm  the  inner  consciousness  moves 
forward  in  time  from  pulse  to  pulse,  from  accent  to 
accent,  in  other  words,  from  moment  to  moment,  from 
now  to  now.  We  shall  analyze  this  forward  move- 
ment in  time,  and  shall  study  the  psychology  of  this 
moment,  this  accent,  this  now;  it  holds  the  secret  of 
music  and  of  common  music-feeling. 

Rhythmic  feeling,  in  obedience  to  the  indwelling 
shaping  principle,  impels  us  to  vary  the  accents  of 
successive  pulses  or  moments  so  that  heavier  accents 
so  alternate  with  lighter  accents  that  they  recur  at 
regular  intervals  of  time,  thus  forming  regular  groups 
and  maintaining  the  rhythmic  balance.  In  the  above 
examples  the  sign  >  indicates  the  heavy  accents,  and 
the  examples  show  that  the  difference  between  one  ele- 
mentary rhythmic  form  and  another  is  a  difference  in 
the  order  of  heavy  and  light  accents.  Thus  the  two 
forms  of  dual  rhythm  are  light-heavy  and  heavy-light, 
while  the  three  forms  of  triple  rhythm  are  light-light- 
heavy,  light-Z^^av^z-light,  heavy -light-light.  All  music- 
rhythms  are  based  upon  these  five  elementary  forms. 
These  accents  of  varying  intensities,  their  regular 
alternations  and  the  recurrent  heavy  accents  are  of 


RHYTHM  AND  TONE  S3 

the  utmost  importance ;  their  psychology  will  discover 
the  hitherto  overlooked  key  to  the  origin  and  true 
nature  of  music's  specific  and  basic  harmony. 

Metre  and  rhythm  are  not  alone  often  confounded, 
but  are  sometimes  treated  as  identical,  which  is  wide 
of  the  truth.  Rhythm  is  not  metre,  metre  is  not 
rhythm,  neither  in  music  nor  in  versification.  Metre 
is  measure  of  rhythm-periods,  that  is,  of  time-periods 
of  tones.  Our  metrical  symbols  are  symbols  of  meas- 
urement; they  symbolize  rhythm,  time.  Metrical  ac- 
cents so-called  do  not  exist.  Feeling  of  rhythm  came 
first,  perception  of  rhythm  came  next,  metrical  and 
numerical  symbols  of  rhythm  came  last. 

21.   Analysis  of  Tone 

Sound  that  wavers  in  pitch  is  unbalanced,  is  unmu- 
sical, is  not  harmonious,  is  not  tone.  Sound  main- 
tained at  an  unwavering  pitch  is  balanced,  musical, 
harmonious,  in  a  word,  is  tone,  the  unique  voice  of 
music.  The  shaping  principle,  equilibrium,  which  is 
inherent  in  common  feeling,  impels  us  to  make  for 
balanced  sound  or  tone  just  as  it  impels  us  to  make 
for  balanced  motion  or  rhythm.  So  long  as  we  main- 
tain sound  at  an  unwavering  pitch,  so  long  do  we  gen- 
erate in  feeling  the  perfect  balance  or  harmony  of 
tone.  This  pure  harmonic  form  of  tone  to  the  genesis 
of  which  in  feeling  music  owes  its  origin  and  exist- 
ence is  the  major  consonance,  music's  first  or  original 
consonance  which  to-day  we  call  the  Tonic-harmony 
of  the  Major  mode,  the  harmony  of  complete  repose. 
This  perfect  tone  or  harmony  opens  the  first  chapter 
of  tone-genesis,  a  new  subject  in  our  science ;  it  is  an 


S4  THE  NATURE  OF  MUSIC 

inner  product  of  feeling,  has  no  existence  outside  of 
feeling  and  now  requires  psychological  analysis.  In 
thought  or  voice  maintain  a  sound  at  an  unwavering 
pitch  and  you  will  generate  this  perfect  tone  or  har- 
mony in  feeling.  Whatever  the  pitch  may  be  the 
result  will  be  the  same.  For  convenience  and  clear- 
ness of  illustration  therefore  we  will  suppose  the  pitch 
to  be  that  of  C.  While  mentally  sustaining  this  tone 
we  are  at  first  conscious  only  of  a  single  tone  as  at  a) 
in  the  example  below.  Analysis  will,  however,  soon 
discover  that  instead  of  sustaining  only  a  single  tone 
we  are  in  truth  sustaining  a  harmonic  complex  of 
tones  comprising  a  root  or  fundamental,  its  major 
third,  pure  fifth  and  octave,  as  shown  below  at  b), 

a)  6)1        3     5      8 


li 


\~~.^^^ 


KJ         .^ 


^ 


To  be  more  explicit,  while  at  first  ,we  are  conscious 
only  of  the  single  tone  C,  which  is  a  root  or  funda- 
mental, analysis  soon  discovers  the  presence  of  a 
third  (E),  a  fifth  (G)  and  an  octave  (C),  which  are 
concomitant  elementary  tones  or  harmonics  and  which 
together  with  the  root  make  up  the  harmonic  form  of 
this  isolated  tone.  Hence  this  truth :  Every  isolated 
tone  is  a  harmonic  complex  of  root  and  elementary 
harmonics,  that  is,  a  composite  of  root,  major  third, 
pure  fifth  and  octave;  in  short,  an  isolated  tone  is 
always  a  major  consonance.  Each  reader  may  verify 
in  and  for  himself  that  this  is  so;  why  it  is  so  will  be 
explained  presently.  The  fact  here  requiring  empha- 
sis is  this:    An  isolated  tone  always  reports  itself 


RHYTHM  AND  TONE  S5 

as  the  root  of  a  major  consonance.  The  word  root 
defines  the  harmonic  relation ;  the  term  major  conso- 
nance defines  the  harmonic /orm.  We  shall  soon  find 
tones  reporting  themselves  as  a  third  or  fifth  of  this 
consonance  and  in  many  other  forms  and  relations. 
In  each  of  these  relations  we  shall  discover  that  the 
tone  arises  in  the  mind  together  with  elementary  har- 
monics, that  the  form  varies  with  the  relation,  that  the 
form  and  relation  of  every  tone  are  therefore  harmonic; 
in  fine,  that  every  tone  is  a  harmony.  Meanwhile  the 
original  major  consonance  requires  further  analysis. 

22.    A  Tone's  Harmonic  Thread 

The  harmonic  complex  which  a  tone  generates  and 
reports  in  common  feeling  may  be  called  the  harmonic 
thread  of  a  tone.  The  harmonies  of  music  form  a 
closely  wrought  web  of  innumerable  harmonic  threads. 
Consciously  and  unconsciously  we  feel  a  tone's  har- 
monic thread,  but  unless  we  accurately  observe  its 
harmonic  thread  we  cannot  appreciate  the  exact  form 
and  relation  of  a  tone.  The  thread  of  the  major  con- 
sonance in  the  above  example  presents  a  root,  third, 
fifth  and  octave.  Each  higher  and  lower  octave  is 
another  root  of  a  like  series  of  harmonics  wherefore 
we  may  change  the  octave-number  8  into  a  root- 
number  1  as  follows:  — 

1351351  1531531 


i 


BSEE^    .    .  -H 


w- 


-^-    *  etc.  *    -^   -I^ 

This  shows  that  the  harmonic  thread  of  a  major 
consonance  extends  through  the  whole  range  of  tone- 


36 


THE  NATURE  OF  MUSIC 


pitch.  Once  generated  in  feeling  we  move  at  pleasure 
up  and  down  from  tone  to  tone  on  this  thread  taking 
the  tones  in  the  above  order  or  making  leaps,  since  in 
doing  this  we  but  follow  the  line  of  least  resistance 
in  obedience  to  the  inherent  shaping  principle,  equi- 
librium. This  first  of  music's  harmonic  threads 
introduced  a  variety  of  intervals  into  experience, 
namely,  the  pure  octave,  fifth  and  fourth,  major  and 
minor  thirds,  sixths  and  tenths,  as  shown  below :  — 


i 


8ve 


5th 


4th 


maj.  3d 


min.  3d 


^ 


-«?- 


-&^ 


maj.  6th        min.  6th       maj.  10th      min.  10th 

^2- 


^^m 


There  is  however  something  vastly  more  important 
than  these  intervals  or  steps  from  tone  to  tone.  It  is 
the  tones  themselves  which  give  rise  to  all  these  inter- 
vals and  which  resolve  themselves  into  three  harmonic 
'perceptSy  namely,  a  root,  a  major  third,  a  pure  fifth. 
Briefly,  each  tone  in  the  above  intervals  is  one  of  these 
three  harmonic  percepts.  The  harmonic  percept  is 
therefore  the  thing  of  primary  importance,  the  essen- 
tial thing  to  understand  and  to  know.  As  we  proceed 
it  will  be  well  to  bear  this  distinction  between  an  inter- 
val and  a  harmonic  percept  in  mind. 

23.    Harmony  in  One  Voice,     Common  Reports 

As  we  have  seen,  the  major  consonance  is  a  complex 
of  three  tones  or  harmonics.  Like  the  root,  each  of 
the  other  two  tones  generates  in  feeling  the  entire 


RHYTHM  AND  TONE 


87 


consonance-thread,  therefore  each  includes  the  other 
two  as  concomitant  elementary  harmonics,  or  briefly, 
as  concomitants.  Thus  the  root  includes  third  and 
fifth  as  concomitants ;  the  third  includes  root  and  fifth 
as  concomitants;  the  fifth  includes  root  and  third  as 
concomitants.  All  three  appear  in  the  following 
melody,  in  each  tone  of  which  we  all  hear  and  feel 
the  same  harmonic  complex  or  form  and  the  same 
harmonic  relation  as  specified  by  the  harmonic  num- 
bers 1,  3,  5  over  the  notes. 

13151351 


^ 


I 


_,fi- 


r^ 


This  provisionally  illustrates  what  I  mean  by  origi- 
nal harmony  in  one  voice,  which  asserts  and  reports 
itself  without  chords.  The  numbers  1,  3,  5  explain 
what  I  mean  by  the  common  reports  of  common  feel- 
ing and  perception,  since  they  faithfully  register  the 
inherent  relations  which  we  all  hear  and  feel  in  com- 
mon. The  number  1  indicates  a  root.  The  numbers 
3  and  5  imply  a  root  and  indicate  the  relation  of  a 
tone  to  its  root.  I  have  said  that  an  isolated  tone 
generates  and  opens  up  its  thread  of  harmony  both 
above  and  below  and  that  we  follow  the  thread  up  or 
down  at  will.  In  the  above  melody  we  move  from 
root  up  to  third,  then  back  to  root,  then  down  to  fifth 
and  so  on.  That  every  tone  arises  in  a  thread  of  har- 
mony is  not  the  only  point  to  be  emphasized.  In  this 
melody  we  are  now  on  a  root,  now  on  a  third,  now  on 
a  fifth  of  a  thread.     The  word  now  is  used  with  pur- 


38  THE  NATURE  OF  MUSIC 

pose.  It  means  that  each  tone  fills  a  moment  in  con- 
sciousness, a  rhythmic  moment  or  period  of  time;  it 
means  that  in  music  a  tone  is  indissolubly  united  with 
rhythm  from  the  moment  it  enters  until  it  makes  its 
exit.  In  its  rhythm  we  find  the  time-relation  of  a 
tone.  In  its  harmonic  thread  we  find  the  pitch-  or 
space-relation  of  a  tone.  Rhythm  or  balanced  motion, 
and  tone  or  balanced  sound,  are  thus  inseparably 
united.  This  union  of  two  balances  or  harmonies 
of  time  and  space,  which  holds  the  secret  of  music's 
original  harmony,  requires  careful  analysis.  This 
moment  of  union,  the  product  of  which  is  pure  har- 
monic tone,  is  an  accentual  moment.  The  principle 
of  harmonic  genesis  I  have  already  named  the  eflScient 
accent. 

The  subject  of  original  harmony  in  one  voice  and 
its  common  reports  here  introduced  may  now  be  more 
fully  illustrated  by  a  few  examples  which  contain 
other  tones,  harmonic  relations  and  harmonic  per- 
cepts which  will  be  explained  in  the  proper  place.  At 
present  it  is  enough  to  demonstrate  that  such  things 
as  harmony  in  one  voice  and  common  reports  really 
exist.  The  first  example  adds  four  other  tones,  a 
number  of  other  harmonic  relations  and  two  other  har- 
monic percepts,  the  minor  seventh  and  major  ninth:  — 

C)     1315335    931^33137353    1 


^■^^-^  Jf  rr^^f^^r^^^ 


crtj''^" ''  'LdJ'Ciircrij''f 


*  The  harmonic  numbers  indicate  either  root  or  relation  to  root.  These 
numbers  are  large  for  major  and  small  for  minor  intervab.  From  Chap.  III. 
L.  E.  K. 


RHYTHM  AND  TONE 


The  next  example  adds  two  chromatics :  — 
135      31^313^35513     5    1 


m 


I 


The  harmonies  and  harmonic  relations  reported  in 
these  melodies  assert  themselves  spontaneously;  they 
are  immutable  because  common  to  all  of  us ;  you  can- 
not change  them  unless  you  add  other  voices  or  chords; 
but  even  though  you  add  only  one  more  voice,  in  so 
doing  you  add  something  of  your  own  choice  and  are 
no  longer  dealing  with  harmony  in  one  voice,  which 
chooses  itself.  In  order  to  understand  the  sequel  it 
is  imperative  that  this  distinction  between  that  which 
elects  itself  and  that  which  you  and  I  elect  should  be 
clearly  apprehended.  The  common  reports  of  self- 
asserting  harmonies  and  harmonic  relations  are  spe- 
cific to  music  in  one  voice,  1  have  made  observa- 
tions for  more  than  twenty  years  and  have  met  no  one 
even  of  moderate  musical  endowment,  whether  child 
or  adult,  whether  student,  musician  or  layman,  who 
did  not  readily  appreciate  a  tone's  inherent  harmony 
and  therefore  harmony  in  one  voice.  For  the  first 
time  in  our  science  we  find  in  these  common  reports 
of  harmony  in  one  voice  the  explanation  of  the  genesis 
and  development  of  tonality  and  of  our  tone-system. 
In  passing  it  may  be  stated  that  our  tonality  and  our 
tone-system  are  inseparably  linked  in  evolution  as 
cause  and  consequence. 


40  THE  NATURE  OF  MUSIC 

24.    Harmonic  Evolution,    The  Major  Tonic 

The  evolution  of  music's  harmonies  beginning  with 
the  genesis  of  the  major  consonance  is  a  psychological 
process  as  beautiful  as  it  is  simple.  Harmonies  have 
succeeded  each  other  one  by  one  in  an  orderly  and 
clearly  traceable  sequence  of  antecedents  and  conse- 
quents, perhaps  the  only  complete  sequence  of  any 
kind  thus  far  presenting  itself  to  psychology  and  there- 
fore of  importance  to  that  science.  Apart  from  origi- 
nal harmony  in  one  voice  and  its  inherent  principles 
this  evolutionary  sequence  of  harmonies  could  not  be 
traced.  Why  ?  Because  harmony  in  one  voice  asserts 
itself  and  its  reports  are  common  reports  and  it  ex- 
cludes the  personal  equation.  When  we  consider  that 
there  is  such  an  evolutionary  sequence  and  that  the 
first  series  of  harmonies  in  this  sequence  is  repeated 
nolens  volens  in  every  developing  musical  mind,  we 
readily  realize  the  signal  importance  of  this  sequence 
alike  to  the  science  and  history  of  music  and  to  music- 
education.  The  harmonies  of  the  individual  tones  in 
the  above  melodies  are  latent  in  all  of  us,  each  tone 
being  a  harmonic  complex  containing  elementary 
harmonics  or  concomitants.  We  have  seen  that  an 
isolated  tone  at  first  appears  to  be  a  single  tone,  that 
later  we  discover  it  to  be  a  complex  of  root,  third  and 
fifth.  This  third  and  fifth  were  always  present  in  the 
tone  as  elementary  harmonics  or  concomitants.  A 
tone  without  concomitants  does  not  exist.  This  third 
and  fifth  were  therefore  latent  in  feeling  and  eventu- 
ally they  were  perceived  and  differentiated,  whereupon 
they  were  expressed  in  melody  and  together  with 


RHYTHM  AND  TONE  41 

their  common  root  became  the  harmonic  basis  of 
tonality.  We  shall  see  that  newly  differentiated  tones 
in  their  turn  generate  new  harmonic  complexes  con- 
taining new  elementary  harmonics  which  in  their  turn 
are  differentiated  and  generate  new  harmonies  with 
new  elementary  harmonics,  and  so  on.  This  psycho- 
logical change  from  latent  feeling  to  perception  and 
expression  roughly  describes  this  evolutionary  process. 
The  tonality  of  the  major  consonance  of  an  isolated 
tone  has  already  been  identified  as  the  Tonic  of  the 
Major  mode.  Alike  we  all  feel  its  purity,  stability, 
repose,  perfect  balance  and  unity;  to  all  it  is  a  centre 
of  gravity,  restful  and  satisfying.  We  have  explained 
all  this  as  due  to  its  perfect  harmonic  form,  this  unique 
form  as  due  to  the  union  of  elements,  this  union  as  due 
to  the  inherent  shaping  principle,  equilibrium.  How- 
ever, the  mere  fact  that  an  isolated  tone  is  always  a 
major  consonance  and  always  the  Major  Tonic,  though 
so  obvious,  does  not  suflfice.  It  requires  explanation. 
Why  does  an  isolated  tone  always  report  this  conso- 
nance ?  To  say  that  the  shaping  principle  is  the  vera 
causa  is  but  a  statement  and  does  not  answer  this 
question.  It  therefore  remains  to  explain  how  this  prin- 
ciple operates,  how  it  shapes  these  harmonies  in  feel- 
ing. The  above  melodies  present  roots,  thirds,  fifths, 
sevenths  and  ninths.  Each  tone  arises  in  a  thread 
of  harmony.  On  certain  tones  the  harmony  changes : 
one  tone  now  reports  itself  a  root  and  now  a  fifth; 
another  tone  reports  itself  now  a  third  and  now  a 
ninth;  another  tone  reports  itself  now  a  seventh  and 
now  a  root.  Analysis  will  show  that  all  these  harmonic 
complexes,  percepts  and  relations  are  due  to  the  in- 


42  THE  NATURE  OF  MUSIC 

fluence  of  rhythm  as  implied  by  the  word  now,  A 
tone  being  an  accentual  moment,  a  series  of  tones  is 
a  series  of  accentual  moments.  We  will  study  and 
analyze  these  accentual  moments.  I  have  already 
said  that  they  hold  the  key  to  the  harmonic  form  and 
relation  of  tone,  which  is  the  secret  of  music.  This 
key  is  latent  in  all  of  us;  all  may  discover  it. 

25.  Rhythmic adence  and  Rhythm-Repose 
The  analysis  of  rhythmic  periods  of  time  is  the  sub- 
ject before  us.  Each  period  is  marked  by  an  accent. 
Some  accents  are  heavier,  some  are  lighter.  Heavier 
and  lighter  accents  alternate  in  such  a  way  that  the 
heavier  accents  recur  regularly  in  time.  These  alter- 
nating accents  are  alternating  accentual  moments. 
Periods  marked  by  heavier  accents  are  called  heavy 
periods,  those  marked  by  lighter  accents  are  called 
light  periods.  Heavy  periods  marked  by  heavier 
accents  are  moments  of  stability,  repose,  balance, 
centres  of  gravity,  moments  of  equilibrium.  Light 
periods  marked  by  lighter  accents  are  moments  of 
instability,  unrest,  unbalance;  they  are  in  relative 
equilibrium,  in  cadence  ;  they  impel  us  to  move  for- 
ward to  a  heavy  period  for  repose,  balance.  Rhythmi- 
cally we  are  therefore  in  cadence  on  lighter  accents,  in 
repose  on  heavier  accents.  This  rhythmic  movement 
of  regularly  alternating  cadence-moments  and  repose- 
moments  is  illustrated  below :  — 


P 

"^^# 

r 

1— 

--/ 

etc. 

1. 

Now 

now. 

now 

now. 

now 

now, 

etc. 

2. 
S. 
4. 

Light 

Cadence 

Unstable 

heavy, 
repose, 
stable, 

light 
cadence 
unstable 

heavy, 
repose, 
stable, 

light 
cadence 
unstable, 

heavy, 
repose, 
stable, 

etc. 
etc. 
etc. 

RHYTHM  AND  TONE  43 

The  four  texts  in  this  example  describe  and  analyze 
our  common  feeling  and  perception  of  elemental  dual 
rhythm.  The  alternating  accentual  moments  marked 
now-now  are  explained  by  the  terms  light-heavy, 
cadence-repose,  unstable-stable  equilibrium.  Rhythm, 
as  I  have  previously  stated,  is  the  universal  form  of 
expression,  all  form  of  expression  being  either  process 
or  record  of  the  rhythmic  accentuation  of  energy 
making  for  equilibrium.  Hence  we  speak  of  the  uni- 
verse as  one  energy,  one  rhythm,  one  equilibrium. 
It  is  common  to  speak  of  accented  and  unaccented 
tones  in  music  and  syllables  in  poetry,  but  in  truth 
there  are  no  unaccented  tones  or  syllables.  Every 
movement  of  energy  in  the  whole  universe,  be  it  ever 
so  slight  and  delicate,  is  an  accent.  Moreover,  all 
movements  are  in  correlation,  wherefore  all  accents  are 
relative  and  the  term  light-heavy  expresses  this  rela- 
tivity. We  cannot  therefore  truly  speak  of  one  move- 
ment or  accent  since  movements  and  accents  succeed 
each  other  periodically  and  are  inseparably  related  as 
light-heavy.  Regular  alternations  of  light  and  heavy 
accents  appear  in  walk  as  well  as  in  march,  in  run  as 
well  as  in  dance,  in  speech  as  well  as  in  song,  in  prose 
as  well  as  in  poetry,  in  all  work  as  well  as  in  all  play, 
in  all  movements  of  body,  mind  and  spirit.  Observe, 
for  example,  the  nondescript  sounds  which  we  spon- 
taneously utter  in  place  of  the  affirmative  yes  and  nega- 
tive no.  The  order  of  relative  accents  in  the  former  is 
light-heavy;  in  the  latter  it  is  the  reverse,  heavy-light. 
These  relative  accents  are  the  same  in  our  expression 
of  yes  and  no  by  a  movement  of  the  head.  In 
nodding  yes  the  head  moves  slightly  backward  on  a 


44  THE  NATURE  OF  MUSIC 

light  accent  and  is  then  brought  forward  on  a  heavy 
accent.  In  no  the  head  is  jerked  to  one  side  on  a 
heavy  accent  and  then  moves  back  on  a  Hght  accent. 
Similar  dual  movements  and  successions  of  relative 
accents  appear  in  our  spontaneous  positive  and  nega- 
tive gestures.  Positive  certainty,  conviction  and  as- 
sertion are  expressed  by  raising  the  hand  on  a  light 
accent  and  bringing  it  down  on  a  heavy  accent.  Un- 
certainty, surprise  and  interrogation  cause  us  to  raise 
the  hands  on  a  heavy  accent,  then  to  relax  and  drop 
them  on  a  light  accent.  Down-accents  are  heavy 
accents  of  positive  gravity. 

This  analysis  shows  that  every  rhythmic  moment  in 
consciousness  is  either  a  repose-moment  or  a  cadence- 
moment.  Rhythm-repose  is  perfect  balance;  rhythm- 
cadence  is  relative  balance  tending  to  perfect  balance. 
This  relation  of  cadence  and  repose  is  inseparable  in 
our  feeling,  percept  and  concept  of  rhythm.  In  other 
words,  there  must  be  a  play  of  light  accent  upon  heavy 
accent,  else  there  is  no  feeling  or  perception  of  rhythm. 
The  play  of  one  light  accent  upon  a  heavy  accent  is  the 
embryonic  form  of  rhythm,  and  a  motive  consisting  of 
two  such  accents  is  the  shortest  conceivable  motive  in 
music.  This  inseparable  relation  of  cadence  and  re- 
pose is  an  important  fact  as  we  shall  presently  see. 
Of  the  two  elements,  rhythm  and  tone,  rhythm  is  first, 
universal  and  fundamental,  while  tone  owes  its  speci- 
fic musical  form  to  rhythm.  Cadence  and  repose  first 
appeared  in  rhythm,  and  their  inseparable  relation  is 
the  basis  of  all  rhythmic  form  and  relation  in  music. 
The  study  of  this  relation  in  tone  is  our  next  step  in 
analysis. 


RHYTHM  AND  TONE  45 

26.    Tone-Cadence  and  Tone-Repose 

Every  tone  in  music  is  in  cadence  or  in  repose. 
Tone-cadence  originated  in  rhythm-cadence.  Tone- 
repose  originated  in  rhythm-repose.  Not  only  are 
tone-cadence  and  tone-repose  directly  derived  from 
rhythm-cadence  and  rhythm-repose,  but  this  relation 
of  cadence  and  repose  is  inseparable  in  tone  as  it  is  in 
rhythm,  it  is  the  basis  and  explanation  of  the  har- 
monic form  and  relation  of  tone  as  it  is  that  of  rhyth- 
mic form  and  relation.  These  truths  assert  themselves 
overwhelmingly  in  our  common  feeling  and  percep- 
tion of  every  measure  of  music;  they  report  them- 
selves moreover  in  every  measure  of  music  in  one 
voice,  in  which  they  first  arose.  The  connection  of  the 
two  truths,  first,  that  all  tones  are  harmonic,  second, 
that  all  tones  are  either  in  cadence  or  in  repose, 
straightway  leads  us  to  the  logical  conclusions  that 
there  is  an  original  cadence-harmony  as  well  as  an 
original  repose-harmony,  and  that  in  their  genesis  these 
two  harmonies  are  inseparably  related,  that  both 
cadence-harmony  and  repose-harmony  arose  one  in 
relation  to  the  other,  in  short,  that  they  arose  together. 
This  inseparable  relation  of  cadence  and  repose  is  the 
key  to  the  mystery  of  harmonic  form  and  relation  of 
tone  called  consonance  and  dissonance,  the  subjects 
of  the  next  chapter,  in  which  the  truth  of  these  conclu- 
sions will  be  subjected  to  the  explanation  and  test  of 
common  reports  of  common  feeling  and  perception. 

The  major  consonance  of  an  isolated  tone  already 
identified  as  the  Tonic-harmony  in  Major  is  the  origi- 
nal repose-harmony,  and  its  three  components  I  name 


46  THE  NATURE  OF  MUSIC 

repose-tones.  Over  and  under  these  repose-tones  and 
in  relation  to  them  have  arisen  four  other  tones  which 
tend,  some  up,  some  down,  into  the  three.  These 
four  are  components  of  the  original  cadence-harmony, 
and  I  name  them  cadence-tones.  Repose-tones  had 
their  genesis  on  heavy  rhythmic  accents,  cadence- 
tones  on  light  rhythmic  accents.  If  it  is  true  that 
cadence-harmony  and  repose-harmony  could  not  have 
arisen  except  in  inseparable  relation  one  to  the  other, 
how  are  we  to  explain  the  undeniable  fact  that  the 
repose-harmony  not  only  came  first  and  was  first 
voiced  in  melody,  but  came  alone  and  unattended  by 
any  other  harmony!  Granting  the  inseparability  of 
the  relation  of  cadence  and  repose  and  the  interde- 
pendence of  their  respective  harmonies,  how  is  it  pos- 
sible to  explain  the  origin  of  the  repose-harmony 
except  it  be  the  direct  result  of  the  resolution  of  a  pre- 
viously existing  cadence-harmony.  This  is  a  subtle 
point,  and  it  strikes  at  the  root  of  the  problem  to  be 
solved.  Subsequent  analysis  will  show  that  the  gen- 
esis of  this  unique  major  consonance  or  repose-har- 
mony was  due  to  the  resolution  of  a  latent  feeling  of 
dissonance  or  cadence-harmony.  The  three  original 
repose-tones  and  four  original  cadence-tones,  which 
together  represent  the  seven  diatonics  of  the  Major 
mode,  are  the  subjects  of  our  next  example:  — 

a)  h)  c) 

13        5        3        5,9 


i 


9 


-Z7- 


-zr 


G>- 


Repose  Group  Cadence  Group  Resolution 


RHYTHM  AND  TONE 


47 


The  Major  Tonic  is  the  root  of  the  original  repose- 
harmony.  The  Major  Dominant  is  the  root  of  the 
original  cadence-harmony.  This  Tonic-thread  com- 
prises root,  third  and  fifth.  The  Dominant-thread 
comprises  root,  third,  fifth,  seventh  and  ninth. 
Though  the  root  of  the  Dominant-thread  is  omitted 
at  b)  and  c)  the  four  cadence-tones  report  this  to 
be  their  common  root  and  harmony  as  the  numbers 
imply.  The  two  subjoined  melodies  include  both 
groups  of  tones,  and  the  accompanying  numbers  indi- 
cate the  common  reports  of  original  harmony  in  one 
voice :  — 

a) 

18         5         3,5  31 


i 


1 


E 


r  r  r  r  'r  r  r  T  r  r  r  V  7 


h) 


r 


^359531     53513      1 


i 


I 


^M=^ 


r 


EZjT 


These  melodies,  like  those  already  presented,  are  but 
provisional  illustrations  of  harmony  in  one  voice  and 
its  common  reports.  We  shall  presently  enter  into 
the  minutest  analysis  of  these  self-reporting  relations 
in  order  to  study  and  explain  their  inherent  principles 
and  laws.  Meanwhile  we  will  note  these  salient 
points:  the  formative  influence  of  rhythm  upon  tone 
and  the  indissolubleness  of  the  two;  the  insepara- 
bility of  the  relation  of  cadence  and  repose,  the 
universality  of  this  relation,  its  appearance  first  in 


48  THE  NATURE  OF  MUSIC 

rhythm,  then  through  rhythm  in  tone;  hence  com- 
posite tone-rhythm,  melody,  music.  Neither  cadence 
nor  repose  can  be  felt,  perceived  or  conceived  except 
in  relation  one  to  the  other,  not  in  rhythm,  not  in 
tone.  Except  for  this  basic  relation  there  would  be, 
could  be,  no  harmonic  form  and  relation  of  tone,  no 
melody,  no  music.  Cadence  seeks  repose,  that  is, 
seeks  resolution  in  repose,  equilibrium.  This  is  illus- 
trated in  the  second  last  example  at  c).  But  resolu- 
tion is  not  a  principle  or  cause,  as  some  theorists 
declare,  nor  is  progression;  ^  the  shaping  principle  and 
causa  causarum  is  equilibrium.  It  may  be  stated  in 
passing  that  music's  great  multiplicity  of  harmonies, 
modes  and  keys  are  derived  from  the  two  original  har- 
monic genera  of  tones,  cadence-harmony  and  repose- 
harmony. 

27.   Melody,  Harmony  and  Rhythm 

Terms  if  not  carefully  defined  lead  to  inevitable  con- 
fusion. The  progress  of  knowledge  under  the  impulse 
of  new  discoveries  modifies  old  and  attaches  new  mean- 
ings to  familiar  terms.  In  the  opening  chapter  I 
pointed  out  the  fallacy  of  the  common  teaching  that 
melody,  harmony  and  rhythm  are  the  three  elements 
of  music  and  have  since  demonstrated  that  melody  is 
not  an  element  in  any  sense  but  is  the  composite  of 
music's  two  elements,  rhythm  and  harmony.  The 
meaning  of  the  term  melody  thus  undergoes  a  complete 
and  unavoidable  change.  In  music  itself  melody  and 
harmony  have  never  been  separable  or  separated.  In 
view  of  this  truth  the  time-honored  separation  of  the 

1  See  The  Septonaie,  Chap.  II.    L.  E.  K. 


RHYTHM  AND  TONE  49 

two  which  still  prevails  as  the  direct  result  of  false 
theories  can  no  longer  be  continued.  Separate  books 
on  melody  and  separate  books  on  harmony  will  be 
valueless  and  will  not  be  written  in  the  future.  Such 
phrases  as  **  the  intimate  connection  between  melody 
and  harmony"  no  longer  have  any  sense.  Never  hav- 
ing been  separable  or  separated,  melody  and  harmony 
do  not  require  connecting.  Another  conception  of 
melody,  namely,  a  conventional  form  constructed 
by  rule  and  composed  of  certain  specified  groups  of 
phrases  in  a  variety  of  ** geometrical  patterns,"  also 
requires  modification,  a  modification  clearly  and  elo- 
quently trumpeted  in  the  works  of  Liszt,  Berlioz  and 
Wagner,  of  Schumann,  Brahms  and  MacDowell. 
Formalism  in  our  classics  has  played  not  only  an 
important  but  an  essential  part  in  music's  evolution 
and  masterpieces.  But  here  we  are  concerned  with 
melody.  Than  its  form,  nothing  could  be  at  once  more 
free  and  more  law-abiding  yet  less  subject  to  any  given 
or  conceivable  code  of  rules.  Melody  is  as  free  as 
thought  and  imagination,  and  its  forms  are  as  limit- 
less as  are  the  forms  of  nature;  it  is  the  essence  of 
music.  Anything  from  a  succession  of  two  tones 
onward  is  a  melody,  a  music-idea,  and  out  of  such 
ideas  do  genius  and  craft  evolve  masterpieces  of  music- 
art.  It  is  jejune  folly  to  say  that  melody  is  exhausted, 
that  new  forms  cannot  be  created. 

The  term  harmony  is  universally  used  in  the  sense 
of  chord,  and  everywhere  the  study  of  harmony  means 
the  study  of  chords.  But  the  accepted  meaning  of 
this  term  is  completely  changed  by  the  discovery  that 
original  harmony  asserts  itself  in  one  voice  without 


50  THE  NATURE  OF  MUSIC 

chords  that  original  harmony  in  one  voice  and  chord- 
harmony  in  several  voices  require  the  most  careful 
distinction,  that  the  former  is  the  evolutionary  fore- 
runner of  the  latter  and  that  the  latter  is  rooted  in  and 
explained  by  the  former.  Harmony  and  chord  there- 
fore can  no  longer  be  regarded  as  synonymous  terms. 
The  identification  of  music's  harmony  and  shaping 
principle  with  universal  harmony  and  the  universal 
shaping  principle  adds  new,  truer  and  deeper  mean- 
ing to  this  term. 

The  new  meaning  and  importance  attached  to  the 
term  rhythm  in  preceding  definitions  and  analyses  can- 
not be  overemphasized.  After  all  it  is  not  so  long  ago 
that  G.  Weber  told  us  that  "rhythm  is  of  no  conse- 
quence." Now  we  discover  that  rhythm  is  at  the 
bottom  of  everything  in  music,  that  the  relation  of 
cadence  and  repose  had  it  not  first  existed  in  rhythm 
could  not  have  appeared  in  tone,  that  cadence  and 
repose  are  two  interdependent  and  inseparable  ele- 
ments at  the  foundation  of  rhythmic  and  harmonic 
relation,  that  rhythm-cadence  and  rhythm-repose  at 
once  explain  the  origins  and  solve  the  problems  of 
form  and  relation,  of  dissonance  and  consonance. 
Therefore  everything  in  music  is  relation  and  has  been 
derived  through  relation.  From  light  to  heavy  accent, 
from  cadence  to  repose,  from  unstable  to  stable  equi- 
librium, such  are  rhythmic  form  and  relation,  such 
through  rhythm  have  arisen  harmonic  form  and  rela- 
tion. 

Elsewhere  I  have  defined  music  as  follows :  Melody, 
the  flower;  harmony,  the  plant  that  bears  the  flower; 
rhythm,  the  root  of  the  plant  that  bears  the  flower. 


RHYTHM  AND  TONE  51 

Although  this  legendary  definition  omits  the  seed, 
tone  or  balanced  sound;  the  nursery,  common  feeling; 
the  potential  life,  energy;  the  inherent  shaping  prin- 
ciple, equilibrium;  and  although  this  definition  is  not 
in  complete  accord  with  the  facts  presented  in  the  fore- 
going pages,  yet  it  has  a  psychological  value  inasmuch 
as  it  indicates  the  true  sequence  of  observation  which 
is  always  the  inverse  of  the  evolutionary  sequence. 
To  explain:  Observation  always  proceeds  from  what 
is  most  apparent  to  what  is  less  and  less  apparent. 
This  inverse  sequence  has  been  followed  by  music- 
observers.  Melody,  the  flower,  was  observed  first, 
was  the  first  subject  of  music-theory.  Next,  but 
yesterday,  came  the  observation  and  theory  of  har- 
mony, the  plant,  in  the  form,  however,  of  chords. 
Then  last  of  all  came  rhythm,  the  root.  In  fact,  the 
scientific  inquiry  by  musicians  into  rhythm  is  so  recent 
that  we  can  truly  say  it  has  just  begun.*  Thus  far 
this  subject  has  been  in  the  hands  of  those  who 
may  be  called  separatists  who  separate  the  insepa- 
rable, namely,  music's  rhythm,  harmony  and  melody. 
Melody  without  harmony,  a  tone  without  harmony, 
are  unfeelable,  unperceivable,  do  not  exist.  The 
moment  of  tone-genesis  being  a  rhythmic  moment  it 
follows  that  rhythm,  harmony  and  melody  have  never 
been  separable  in  feeling.  Because  this  inseparability 
was  not  perceived,  rhythm,  harmony  and  melody 
were  separated  in  theory,  but  not  in  practice.  To- 
day they  are  united  in  common  feeling,  and  it  is  safe 
to  postulate  that  they  always  have  been  united.  We 
judge  of  what  has  been  by  what  is.  The  music  of 
to-day  is  connected  with  the  music  of  all  the  past  in 


52  THE  NATURE  OF  MUSIC 

a  sequence  of  effects  and  causes,  each  cause  being  the 
effect  of  a  previous  cause.  I  have  proved,  and  will 
adduce  further  proof,  that  melody  is  the  composite  of 
rhythm  and  harmony.  This  is  nothing  new  to  music- 
feeling  where  melody  always  has  been  a  composite, 
but  it  is  new  to  theory  and,  owing  to  its  discovery  of 
harmony  in  one  voice,  completely  changes  the  point  of 
view  of  theory. 

Knowledge  is  evolution  of  perception.  Truth  per- 
sistently knocks  at  the  door  of  consciousness,  sure  of 
being  admitted  sooner  or  later  to  enrich  the  store  of 
knowledge  and  experience. 


CHAPTER   III 

ORIGINAL  DISSONANCE  AND  CONSONANCE  IN  ONE  VOICE 

28.    Genesis  of  the  Major  Consonance^  Music's 
First  Regnant  Harmony 

The  fundamental  forms  of  tone  are  dissonance  and 
consonance.  Both  are  products  of  feeling,  both  first 
arose  in  one  voice,  both  are  offsprings  of  the  elemen- 
tal relation  of  rhythm-cadence  and  rhythm-repose. 
Briefly, /orm  is  derived  from  relation^  the  forms  of  dis- 
sonance and  consonance  from  the  rhythmic  relation 
of  cadence  and  repose.  This  truth  lifts  the  veil  of 
mystery  which  has  hitherto  hidden  from  view  the  true 
nature  and  origin  of  dissonance  and  consonance. 
What  man  did  not  feel  he  could  not,  it  is  safe  to  say, 
did  not  express,  and  music  from  first  to  last  is  a  crea- 
tion and  expression,  of  music-feeling.  Man's  first  ex- 
pression of  tone  was  admittedly  in  song.  We  will 
study  these  first  utterances. 

The  first  attempts  to  pitch  a  tone  comprise  two 
moments  of  time:  first,  a  sliding;  second,  an  arriving.- 
These  two  moments,  previously  described  as  now- 
noWy  light-heavy,  cadence-repose,  unstable-stable,  are 
two  correlated  and  interdependent  rhythmic  accents 
which  are  inseparable  in  feeling,  perception  and  con- 
ception. Of  the  two,  the  first  is  tend^  the  second  is 
end;  the  first  resolves  into  the  second,  the  second  is 
attainable  only  through  the  first,  since  apart  from  the 
feeling  of  tend  there  is  no  feeling  of  end.     Below  I 


54  THE  NATURE  OF  MUSIC 

indicate  cadence  or  tend  by  a  wave-line  which  resolves 
into  repose  or  end  as  shown  by  a  straight  line :  — 


-Bepose 
Cadence 

The  first  or  sliding  moment  in  pitching  a  tone  is 
cadence,  unstable  equilibrium,  relative  harmony,  tend ; 
in  it  the  entire  cadence-thread  of  harmony  is  potentially 
present.  The  second  or  arriving  moment  is  repose, 
stable  equilibrium,  perfect  harmony,  end;  in  it  the 
entire  repose-thread  of  harmony  is  potentially  present. 

Feeling  thus  resolves  wavering  into  unwavering 
pitch,  unstable  into  stable  equilibrium,  relative  har- 
mony into  perfect  harmony,  apparent  chaos  into  per- 
fect order  and  unity,  a  light  accent  into  a  heavy  accent, 
cadence  into  repose,  aspiration  into  attainment,  tend 
into  end,  latent  feeling  of  dissonance  into  consonance. 

This  heavy  accent  of  rhythm  I  have  already  named 
the  efficient  accent  of  tone-genesis,  that  is,  of  the  genesis 
of  harmony.  This  end  of  tend  was  the  genesis  of 
music's  first  tone,  the  birth  of  music  itself,  of  melody. 
This  first  tone  was  not  only  the  first  harmony,  but  was 
the  first  regnant  harmony  generated  by  the  efficient 
accent.  This  first  harmony  is  the  genus  consonance, 
our  Major  Tonic-harmony. 

The  power  to  place  a  tone  in  the  voice  and  to  express 
exact  pitch  was  acquired  through  the  evolutionary 
process  of  resolution  above  described.  In  the  first 
crude  attempts  at  pitch  the  entire  process  of  sliding 
and  arriving  is  intoned.     But  when  the  power  to  ex- 


DISSONANCE  AND  CONSONANCE  55 

press  exact  pitch  has  been  acquired  the  first  or  sliding 
part  of  the  process  is  carried  out  silently.  Though 
when  trained  we  place  tones  automatically,  neverthe- 
less the  voice  has  to  be  adjusted  to  each  tone,  infinitesi- 
mally  short  though  this  moment  of  adjustment  may  be. 
The  process  of  resolution  just  analyzed  explains 
why  when  we  pitch  an  isolated  tone  we  invariably 
make  for  the  eflScient  accent  and  generate  in  feeling 
the  repose-thread  of  the  original  major  consonance, 
our  Major  Tonic-harmony,  music's  first  regnant  har- 
mony, as  follows: — 

o)  b)  e) 

1351        1351  1351 


i 


i^i'  .  >>  -  [*^i^^ 


w 


The  origin  of  this  genus  consonance  is  now  ex- 
plained. How  and  why  this  gr^ni^^-harmony  came 
first  is  now  explained.  Its  genesis  is  due  to  the  reso- 
lution of  the  latent  Reeling  of  dissonance  (relative  har- 
mony) into  the  major  consonance  (perfect  harmony). 
The  operative  cause  is  the  efficient  accent  which  on 
the  line  of  least  resistance  makes  for  complete  equi- 
librium. Briefly,  the  efficient  accent  is  the  cause  of 
resolution.  Man  first  felt  and  expressed  the  relation  of 
cadence  and  repose  rhythmically,  but  when  he  joined 
sound  to  this  rhythmic  relation  he  eventually  evolved 
the  feeling  and  expression  of  tone-cadence  and  tone- 
repose.  Tone-cadence  is  dissonance,  it  first  arose  in 
one  voice.  Tone-repose  is  consonance,  it  first  arose 
in  one  voice.  How  music's  original  dissonance  arose 
in  relation  to  music's  original  consonance  will  be 
considered  presently.    Meanwhile,  it  may  be  observed 


56  THE  NATURE  OF  MUSIC 

that  music  springs  from  one  source,  not  from  two 
sources.  At  the  basis  of  music  there  is  unity,  not  a 
duahty  as  many  think  and  teach.  Music  started  with 
one  harmony,  the  Major  Tonic-harmony,  and  all  sub- 
sequent harmonies  are  traceable  through  a  chain  of 
relations  back  to  the  first.  Major  and  Minor  are  two 
modes,  but  Major  preceded  Minor  and  Minor  was 
derived  from  Major.  Major  and  Minor  are  therefore 
not  two  tonalities,  they  are  two  modes  of  one  tonality, 
hence  the  unity  of  tonality.  Tonality  is  the  sum  of 
tone-relations,  and  music  began  the  development  of 
tonality  with  the  regnant  Tonic-harmony  of  the  Major 
mode.  Again:  rhythm  and  harmony  are  two  ele- 
ments, but  in  tone,  in  melody,  in  music,  the  two  are 
indivisible,  one,  hence  unity.  If  there  be  any  duality 
it  should  be  cadence  and  repose.  But  is  this  duality  ? 
No.  Cadence  and  repose  are  the  two  inseparable 
and  interdependent  elements  of  the  unity  relation. 

The  simplest  songs  of  birds,  the  simplest  specimens 
of  primitive  human  music,  the  improvised  songs  and 
intoned  calls  of  children,  the  intoned  cries  of  street- 
venders,  all  these  songs,  calls  and  cries  are  based  upon 
the  genus  consonance,  our  Major  Tonic-harmony. 
Since  in  evolution  birds  antedate  man,  we  may  assume 
that  the  birds  were  the  first  singers,  concert-givers  and 
music-teachers.  Japan,  for  example,  has  few  or  no 
singing  birds,  therefore  no  feathered  music-teachers. 
Perhaps  this  explains  why  Japan  is  a  nation  without 
song.  From  a  collection  of  bird-songs  observed  by 
me  and  accurately  written  both  as  to  rhythm  and 
harmony,  a  few  are  here  selected  and  arranged  in 
three  groups  which  exemplify  three  stages  of  develop- 


DISSONANCE  AND  CONSONANCE 


57 


ment  from  simple  to  more  and  more  complex.     The 
first  group  marks  an  early  stage  in  which  only  the 
tones  of  the  Major  Tonic-harmony  appear. 
1.  2.  3. 

53535161  5 


8. 


1    5  3  3  5   1 


3   5 


^ 


■>{  f  f  I  ^r^j 


^s 


m 


ipzz^c 


-• — • — 0- 


9. 


11111 


^^^^^^ 


The  next  group  adds  two  cadence-tones,  marked  x, 
to  the  regnant  Tonic-harmony. 
1.  2. 

151535     1  51513535 


^tf-!\'  i\sr^:iv:\'  rj'iH 


i 


35    353      535 


^ 


I 


The  appearance  of  the  above  cadence-tones  marks 
a  more  advanced  stage  of  development.     A  much 


58 


THE  NATURE  OF  MUSIC 


higher  stage  is  exemplified  in  the  next  group  of  songs 
which  introduce  two  additional  regnant  harmonies, 
namely,  the  Dominant-harmony  (marked  V)  and  the 
Subdominant-harmony  (marked  IV),  both  of  which 
arise  in  relation  to  the  Tonic-harmony  (marked  I). 


2. 
5    5     5 


3. 


551     35555 


i 


i 


I^P^S 


ga 


V     V 


r    r  if  r  r  ^^ 


6. 


i 


1     5 


^ 


£: 


3 


^ 


6. 


3     13    13     5 


i^ 


i 


^ 


IV  I 

In  these  few  bird-songs  the  harmonic  basis  of  music 
is  plainly  revealed,  and  the  subject  of  tone-relations  is 
fully  opened  up.  The  harmonic  numbers  symbolize 
the  common  reports  of  inherent  relations.  The  har- 
monic analysis  of  the  cadence-tones  and  cadence- 
harmonies  and  the  connection  of  the  successive  stages 


DISSONANCE  AND  CONSONANCE 


59 


of  development  here  suggested  will  engage  our  atten- 
tion later  on.  Also  for  future  reference  I  here  add 
three  more  bird-songs,  the  first  two  of  which  report 
the  Minor  consonance  and  mode,  while  the  last  intro- 
duces a  chromatic  marked  by  a  star. 
1.  2. 


i^^ 


m 


s 


^ — i^ — ^ 


± 


ms-^if  t  I'f  n 


I  *      V 

In  their  first  efforts  to  discriminate  the  concomitant 
harmonics  of  an  isolated  tone,  students  most  frequently 
feel  and  express  the  octave  first,  next  the  fifth,  last  of 
all  the  third,  as  follows :  — 

1115      13orll5      31 


I 


I 


k± 


The  psychological  law  here  operative  is  this.  The 
closer  the  proximity  of  tones  the  more  difficult  is  it  to 
perceive,  differentiate  and  express  them.  By  impli- 
cation the  larger  intervals  were  expressed  first,  the 
smallest  last.  Thus  octaves,  fifths  and  fourths,  thirds 
and  sixths  came  before  the  whole  step,  and  last  of  all 
came  the  half  step.  All  the  first-named  intervals  are 
present  in  the  Major  Tonic-thread  of  harmony  and 
appear  in  the  first  group  of  the  above  bird-songs.  The 
cadence-tones  in  the  second  and  third  groups  of  these 


60  THE  NATURE  OF  MUSIC 

songs  exemplify  the  introduction  of  the  whole  step  and 
half  step.  The  evolutionary  sequence  of  regnant  har- 
monies begins  with  the  Major  Tonic.  The  evolu- 
tionary sequence  of  intervals  begins  with  the  intervals 
formed  by  the  tones  of  this  first  regnant  harmony. 
The  Major  Tonic-harmony  is  the  only  harmony  which 
has  entered  into  consciousness  hy  way  of  its  root. 
We  shall  see  that  the  Dominant-harmony  was  intro- 
duced by  its  fifthy  the  Subdominant-harmony  by  its 
third. 

While  we  may  affirm  with  certitude  that  the  Major 
Tonic-harmony  was  the  first  of  all  harmonies,  we  can- 
not tell  what  was  its  exact  pitch  or  key,  simply  because 
we  do  not  know.  However,  the  terms  Major  and 
Tonic  imply  mode,  relation,  tonality  and  also  relative 
pitch  but  not  fixed  pitch,  since  this  Major  Tonic  arises 
on  any  isolated  tone  of  any  pitch.  Like  the  birds  we 
sing  melodies  and  correctly  express  their  inherent  har- 
monic relations  or  tonality,  completely  unconscious  the 
while  of  fixed  pitch  or  key,  although  we  are  expressing 
key-relations.  Fixed  pitch  is  indicated  when  we  say 
C  Major,  D  Major,  E  Major,  and  so  on,  by  which  we 
mean  that  the  Major  Tonic  is  pitched  or  keyed  on 
C,  D,  E,  wherefore  the  notes  C,  D,  E  are  called  key- 
notes and  wherefore  the  terms  keynote  and  Tonic  are 
used  interchangeably.  Because  the  feeling  of  the 
harmonic  relations  we  call  tonality  are  common  to  all 
of  us,  because  they  underlie  all  music  of  bird  and  man, 
because  they  would  exist  even  though  systems  of  fixed 
pitch  and  notation  had  never  been  invented  and 
adopted,  because  they  are  the  essential  thing  to  appre- 
ciate and  know,  because  our  complex  system  of  nota- 


DISSONANCE  AND  CONSONANCE  61 

tion  so  completely  conceals  the  unity  and  simplicity 
of  harmonic  tonality,  for  these  and  other  reasons  un- 
necessary to  mention,  nothing  could  bring  us  closer  to 
these  innate  relations,  or  prove  a  greater  desideratum 
and  simplification  than  a  set  of  symbols  which  dis- 
regards any  fixed  pitch  and  which  is  uniformly  the 
same  in  every  key.  The  syllables  do,  re,  mi,  etc.,  sup- 
ported by  the  harmonic  numbers  adduced  from  ori- 
ginal harmony  in  one  voice  fully  meet  the  case. 
Music's  first  harmony  and  germs  consonance,  our 
Major  Tonic-harmony,  is  now  presented  thus :  — 

13  5 

do  mi sol 


We  may  say  with  certitude  that  do  was  the  first 
Tonic  and  root,  that  mi  was  the  first  major  third  and 
that  sol  was  the  first  pure  fifth.  These  are  the  only 
three  tones  and  harmonic  percepts  in  our  first  group 
of  bird-songs.  In  the  second  group  of  songs  note  the 
first  cadence-tones,  re  and  la,  the  former  as  fifth  intro- 
ducing the  Dominant-harmony,  the  latter  as  third 
introducing  the  Subdominant-harmony.  But  we  are 
advancing  too  fast  and  will  next  consider  the  origin  of 
the  genus  dissonance. 

29.    Genesis  of  Cadence-Harmony  or  Original 
Dissonance  in  One  Voice 

We  say  that  a  leading-tone  tends  up,  a  seventh  tends 
down.  Tend  is  cadence;  its  objector  end  is  repose. 
No  chord  is  required  to  generate  and  illustrate  this  re- 


62  THE  NATURE  OF  MUSIC 

lation,  since  it  reports  itself  in  one  voice  as  exemplified 
below :  — 

3      1       5^       f^S        .T^        9^ 

ti— -do         re— —do         re  -—"mi  fa"**- mi  la«i«^sol 


^ —  — =^=^^       .^^-4J 


F 


r 


-r  t-~r  ^"^    f^ 


Cadence  connotes  cadence-harmony,  dissonance, 
incompleteness,  hence  the  tend  to  repose  in  the  above 
cadence-tones  i%  re,  /a,  la.  Repose  connotes  repose- 
harmony,  consonance,  completeness,  hence  no  tend 
but  an  end  as  reported  by  the  above  repose-tones  do, 
mi,  sol.  Our  example  presents  no  chords,  but  it  does 
present  harmonies,  since  each  tone  arises  in  the  mind 
together  with  concomitant  harmonics  and  is  therefore 
a  harmony.  Thus  a  cadence-tone  reports  one  har- 
mony, a  repose-tone  reports  another  harmony,  and 
the  resolution  of  one  tone  into  another  is  the  resolution 
of  one  harmony  into  another.  Were  it  not  for  the 
inherent  harmony  of  tone  there  would  be  neither  the 
feeling  of  cadence  nor  the  feeling  of  repose,  no  form 
and  relation  of  tone  in  the  musical  sense.  Because  of 
this  harmonic  form  and  relation  inseparable  in  tone  we 
all  share  in  the  common  feeling  of  the  above  cadences, 
of  harmony  and  harmonic  relation,  of  dissonance  and 
consonance  in  one  voice. 

Our  example  introduces  four  cadence-tones  ti,  re, 
fa,  la  in  addition  to  the  three  repose-tones  do,  mi,  sol. 
These  four  cadence-tones  are  components  of  the  genus 
dissonance;  they  lie  directly  over  and  under  the  three 
repose-tones  of  the  genus  consonance  in  relation  to 


DISSONANCE  AND  CONSONANCE  63 

which  they  first  arose.  In  correlation  the  repose-tones 
of  the  genus  consonance  report  do  as  common  root  or 
root  of  this  genus.  In  correlation  the  cadence-tones 
report  sol  to  be  their  common  root  and  the  root  of  the 
genus  dissonance.     Examples  follow:  — 


1 

do 

5 

sol 

3 

mi 

1         9 

do            la 
1 

7 

fa 

5 

re 

3 

ti 

1 
sol 

1. 

Genus  Consonance. 

19- 

Root 

2. 

Genus  Dissonance. 

Root 

The  genus-rooi  do  is  the  Major  Tonic.  The  genus- 
root  sol  is  the  Major  Dominant.  Tones  are  ninths  or 
sevenths  or  fifths  or  thirds  or  roots  of  harmonic  threads, 
and  the  number  over  each  indicates  a  root  or  relation 
to  root.  Sol  first  arose  as  fifth  in  the  genus  conso- 
nance, thereafter  asserted  itself  as  root  of  the  genus 
dissonance.  Sol  is  therefore  the  first  nexus,  common 
tone  or  bond-tone  of  two  harmonies,  since  it  connects 
the  two  genera,  dissonance  and  consonance,  as  shown 
below:  — 


9^53       fl  6]      3        1 

la  fa  re  ti  sol  sol  mi  do 


^^m 


ij 


Bond-tone 
Dissonance  Consonance 


The  origin  in  rhythm  of  the  inseparable  relation  of 
cadence  and  repose,  the  consequent  genesis  of  the 


64  THE  NATURE  OF  MUSIC 

latent  feeling  of  dissonance  and  consonance,  and  the 
genesis  of  consonance  through  the  resolution  of  this 
latently  felt  dissonance,  these  important  points  were 
explained  in  the  foregoing  section.  One  by  one  these 
latent  cadence-tones  of  dissonance  were  perceived, 
differentiated  and  expressed.  First  of  these  to  appear 
in  melody  were  the  whole  steps  re  in  relation  to  do  and 
rriiy  la  in  relation  to  soL  Much  later  came  the  half 
steps  ti  in  relation  to  do,  Ja  in  relation  to  mi.  In  our 
example  of  cadences  re  tends  down  to  do  and  up  to  mz, 
la  tends  down  to  sol,  fa  tends  down  to  mi,  ti  tends  up  to 
do.  For  practical  and  theoretical  reasons  too  obvious 
to  require  mention  I  name  ti  the  upleader,fa  the  down- 
leader. 

The  evolutionary  sequence  of  cadence-tones  in  this 
order,  namely,  re,  la,  fa,  ti,  is  supported  by  history  in  its 
records  of  primitive  scales  and  melodies.  As  evidence 
witness  the  so-called  great  scale,  small  scale  and  the 
pentatonic  scale  in  which  the  great  and  small  scales 
are  united.  In  these  scales  there  are  no  half  steps, 
since  fa  and  ti  do  not  appear.  All  are  given  and 
analyzed  below:  — 

1.  Great.  2.      Small.        3,      Pentatonic. 

153        5315      3       5      3^-)<> 

do        re        mi         sol  la         do        re         mi        sol         la 


i 


i 


r  r  c   I — I    r  f  r   I — 

The  harmonic  numbers  indicate  the  common  re- 
ports of  original  harmony  verified  by  common  percep- 
tion.    The   Major   Tonic-harmony   is   regnant,    the 


DISSONANCE  AND  CONSONANCE  65 

tones  re  and  la  cadence  up  and  down  into  do-mi-sol, 
the  regnant  harmony.      Ascend  or  descend  on  this 
pentatonic  scale  in  every  conceivable  rhythm,  yet  the 
harmonic  relations  remain  unchanged.     However,  the  ^ 
analysis  of  a  scale  has  little  purpose,  for  a  scale  is  but  a 
record  of  tones  in  use  during  a  certain  period  of  his- 
tory; briefly,  scales  are  so  many  tone-systems  of  his- 
tory.    What  is  of  essential  importance  is  the  analysis 
of  the  melodies  which  are  responsible  for  these  tone- 
systems  the  progressive  development  of  which  has 
resulted  in  our  present  complex  system.     Thus  far  we 
have  accounted  for  and  exemplified  but  one  regnant 
harmony,  the  Major  Tonic.     How  a  second  and  a 
third  regnant  harmony  were  generated  are  subjects 
presently  to  be  considered.     Here  an  important  fact^ 
to  which  we  shall  revert  later  on  may  be  mentioned.    I 
It  is  this :  During  the  regnancy  of  the  Major  Tonic-    I 
harmony  la  always  reports  itself  as  third  of  /a,  while    I 
the  remaining  tones  of  the  germs  dissonance  during     | 
this  regnancy  of  the  Tonic  always  report  themselves 
in  their  ^^Tii^^-relations,  ti  as  third,  re  as  fifth,  fa  as 
seventh  of  sol,  the  Dominant.     La  reports  itself  as 
ninth  only  during  the  regnancy  of  the  Dominant- 
harmony,  which  is  the  genus  dissonance.    The  tone  la, 
as  we  shall  see,  plays  a  leading  and  significant  part  in 
the  development  of  harmony  and  tonality. 

The  above  explanations  of  the  genesis  of  the  four 
cadence-tones  and  the  order  of  sequence  in  which 
they  arose  are  further  supported  by  deduction  and  by 
induction ;  by  deduction  from  the  principles  of  causa- 
tion and  harmonic  genesis  set  forth  in  these  pages, 
by  induction  through  data  derived  from  exact  analysis 


66  THE  NATURE  OF  MUSIC 

of  bird-music,  primitive  music,  music-feeling  and 
progressive  mental  development  in  music.  I  say 
exact  analysis  advisedly,  since  in  the  past  no  basis  for 
exact  analysis  of  primitive  music  and  common  music- 
feeling  has  been  discovered.  For  the  first  time  in  the 
history  of  music-science  such  a  basis  presents  itself 
in  original  harmony  in  one  voice.  The  principles, 
causes  and  conclusions  thus  far  presented  and  exem- 
plified are  directly  due  to  the  discovery  of  original  har- 
mony in  one  voice,  and  its  incontrovertible  evidence  in 
the  common  reports  of  common  feeling  and  percep- 
tion. Thus  original  harmony  and  its  common  reports 
place  all  observers  and  analysts  on  common  ground, 
a  common  basis  from  which  to  make  observations  and 
draw  conclusions  from  such  observations,  a  point  of 
view  at  once  new  and  common.  Dissonance  and 
consonance,  the  most  fundamental  and  perplexing, 
therefore  the  foremost  problem  of  music-science,  have 
remained  a  mystery,  an  unsolved  problem,  and  now 
find  a  simple  solution  through  original  harmony  and 
its  common  reports.  Some  musicians  may  object  as 
follows:  Everybody  knows  that  dissonance  and  con- 
sonance did  arise  and  are  at  the  foundation  of  music, 
that  the  cadence-tones  not  only  did  appear  over  and 
under  the  three  tones  of  the  Tonic  chord,  but  arose 
in  relation  to  this  Tonic-triad  and  came  to  stay.  The 
facts  are  self-evident.  Why  not  stop  here  and  be  satis- 
fied ?  It  is  otherwise  with  the  scientific  observer  who 
seeks  causes;  he  cannot  stop  and  has  no  rest  until  he 
finds  the  causes  that  explain  how  forms  and  relations 
came  to  be  what  they  are.  Our  story  of  genesis  is 
simply   this.     In   obedience    to   inherent   principles 


DISSONANCE  AND  CONSONANCE  67 

rhythm  and  tone  met,  merged  and  became  one,  then 
rhythm-cadence  and  rhythm-repose  became  tone- 
cadence  (dissonance)  and  tone-repose  (consonance), 
and  forever  after  there  was  music. 

The  foregoing  analyses  and  examples  conclusively 
prove,  first,  that  original  harmony  is  harmony  in  ane 
voice,  that  tones  are  heard,  felt  and  expressed  in  ca- 
dence or  repose  as  roots  or  thirds  or  fifths  or  sevenths 
or  ninths,  that  tone  and  tone-relation  connote  har- 
mony and  harmonic  relation,  that  harmonic  form  and 
harmonic  relation  in  one  voice  are  self-asserted,  fixed 
and  immutable,  and  by  implication  that  the  reports 
of  original  harmony  are  common  reports ;  second,  that 
dissonance  like  consonance  had  its  genesis  in  one 
voice,  that  the  genus  dissonance  and  the  genus  con- 
sonance are  respectively  the  harmonies  of  the  Major 
Dominant  and  Major  Tonic,  and  by  implication  that 
tonality  is  fundamentally  and  wholly  a  question  of 
harmony,  and  that  original  harmony  in  one  voice  is 
its  basis;  third,  that  the  Major  Tonic  was  the  first 
regnant  harmony,  and  this  implies  the  priority  of 
Major  tonality  ;  fourth,  that  melody  instead  of  being 
an  element,  as  generally  supposed,  turns  out  to  be  a 
composite  of  rhythm  and  harmony,  and  by  implica- 
tion that  melody  is  the  original  vehicle  of  dissonance, 
consonance  and  tonality,  in  short,  of  music  per  se  ; 
in  fine,  that  dissonance  is  neither  more  nor  less  a  har- 
mony than  consonance,  the  former  being  unstable  and 
relative  equilibrium,  the  latter,  stable  and  perfect 
equilibrium.  ^ 


68  THE  NATURE  OF  MUSIC 

30.   Distinction  between  Original  Harmony  in 
One  Voice  and  Chord-Harmony 

Music-history  everywhere  identifies  the  beginning 
of  harmony  with  the  first  use  of  chords.  Every 
treatise  on  harmony  is  a  treatise  on  chords.  The 
concurrence  of  at  least  two  tones,  therefore  a  chord,  is 
everywhere  considered  indispensable  to  the  percep- 
tion, conception  and  presentation  of  a  consonance  and 
a  dissonance.  Everywhere  the  study  of  harmony  and 
harmonic  analysis  means  the  study  of  chords  and 
chord-analysis,  and  no  other  basis  having  been  dis- 
covered, the  chord  is  everywhere  regarded  as  the  basis 
of  harmony.  These  facts  plainly  show  that  the  con- 
ception of  harmony  as  chord  is  universal.  The  rea- 
sons for  my  dissent  from  this  common  view  are  rooted 
in  the  following  facts  and  conclusions.  The  chord  is 
Si  form  of  harmony,  but  is  not  the  original  form,  there- 
fore the  chord  is  not  the  basis  of  harmony.  The 
original  form  is  the  basis,  it  is  dissonance  (cadence) 
and  consonance  (repose)  in  one  voice.  The  concur- 
rence of  two  or  more  tones,  that  is,  a  chord,  is  not 
requisite  to  hearing,  feeling,  perceiving,  conceiving 
and  presenting  a  dissonance  and  a  consonance.  A 
single  tone  suflices  for  all  this  since,  as  has  been 
demonstrated,  each  of  a  series  of  single  tones  is  a  dis- 
sonance or  a  consonance.  Harmony  is  a  discovery, 
not  a  "modern  invention"  as  Spencer  declares. 
Original  harmony  in  one  voice,  old  as  music  itself 
and  belonging  to  all  time,  is  the  spontaneous  product 
of  feeling;  it  antedates  chord-harmony  and  belongs 
to  the  historic  and  prehistoric  periods  of  homophony. 


DISSONANCE  AND  CONSONANCE  69 

Chord-harmony,  on  the  other  hand,  is  a  compara- 
tively recent  product,  a  product  of  reflection  and 
theory,  and  its  roots  reach  deep  down  into  original 
harmony  from  which  it  is  a  psychological  evolution. 
Though  their  connection  has  so  long  remained  con- 
cealed, it  is  safe  to  infer  that  the  two,  original  harmony 
and  chord-harmony,  have  never  been  separated  in 
feeling,  and  that  the  feeling  of  the  former  has  ever 
directed  and  guided  the  course  of  development  of  the 
latter.  The  feeling  of  original  harmony  in  one  voice, 
being  the  universal  and  basic  harmonic  sense,  may  be 
designated  as  the  common  harmonic  sense.  The  truth 
of  this  is  demonstrated  and  proved  by  the  common 
reports  of  common  feeling  and  perception. 

The  common  view  of  the  chord  as  the  only  form  and 
as  the  basis  of  harmony  has  not  alone  created  much 
confusion  in  the  theories  of  music,  but  its  general  ac- 
ceptation as  an  ultimatum  has  acted  as  a  check  upon 
scientific  research.  The  questions  What  is  music  ?  and 
What  is  common  music-feeling  ?  so  often  set  aside  as 
insoluble  mysteries,  are  not  separable  since  the  answer 
to  the  first  lies  hidden  in  and  awaits  the  answer  to  the 
second.  But  these  primary  questions  could  not  be 
answered  until  the  solution  of  the  basic  problem  of 
consonance  and  dissonance  had  been  discovered  and 
a  theory  of  music  based  on  this  solution  had  been  ex- 
pounded. The  curious,  among  whom  I  count  myself 
as  most  curious,  may  well  ask  why  so  simple  a  solu- 
tion of  the  problem  as  that  of  cadence  and  repose  in  one 
voice  has  so  long  remained  concealed.  This  oversight 
may  be  assigned  to  two  principal  causes  and  fallacies 
already  suggested:  first,  to  the  chord-basis  of  har- 


70  THE  NATURE  OF  MUSIC 

mony;  second,  to  the  persistent  and  futile  attempts  to 
base  the  theory  of  music  on  physical  acoustics.  There 
are  three  evolutionary  chapters  of  harmony  which  may 
be  provisionally  indicated  here. 

1.  Homophonic  Harmony.  This  is  original  har- 
mony in  one  voice,  which  is  the  inherent  harmony  of 
single  melodies.  By  single  melodies  I  mean  all  music 
in  one  voice.  This  chapter  represents  the  primary 
age  of  music. 

2.  Polyphonic  Harmony.  This  is  the  inherent 
harmony  of  combined  melodies,  that  is,  of  two,  three 
or  more  coincident  melodies.  This  chapter  may  also 
be  called  contrapuntal  harmony  and  constitutes 
music's  middle  age. 

3.  Chord-harmony.  This,  the  only  form  thus  far 
recognized,  is  the  supporting  and  accompanying  har- 
mony of  single  and  combined  melodies.  This  chapter 
represents  music's  modern  age. 

These  three  chapters  and  corresponding  ages  over- 
lap; they  mark  a  psychological  advance  from  simple 
to  complex  and  from  the  indefinite  to  the  definite ;  they 
correspond  to  the  three  psychological  stages  of  music's 
childhood,  adolescence  and  maturity.  The  golden 
thread  by  which  all  these  forms  of  harmony  are  con- 
nected in  evolution  has  preserved  only  what  was  favor- 
able and  useful,  so  that  in  modern  music  all  three  are 
employed  in  composition.  The  distinction  here  under 
consideration  may  now  be  carried  a  step  farther. 

Original  harmony  (one  voice  always  understood)  is 
natural  harmony  by  natural  selection.  Chord-har- 
mony is  personal  harmony  by  personal  selection.  The 
forms  of  original  harmony  select,  assert  and  present 


DISSONANCE  AND  CONSONANCE  71 

themselves ;  in  any  single  melody  they  are  identical  in 
all  of  us,  they  are  completely  free  from  personal  selec- 
tion and  therefore  from  the  personal  equation.  Con- 
cisely stated,  personal  selection  cannot  enter  into 
original  harmony,  in  which  the  forms  are  uniformly 
the  same.  In  chord-harmony,  on  the  other  hand,  we 
are  compelled  to  make  a  personal  selection  not  only  of 
this  or  that  series  of  specific  constituent  chords,  but  also 
of  the  number  of  voices  to  be  employed.  Briefly,  a 
melody  may  be  chorded  in  many  ways  while  the  origi- 
nal harmony  of  a  melody  is  uniformly  the  same.  Thus 
it  is  clear  that  the  forms  of  original  harmony  are  im- 
mutable since  they  cannot  be  changed  except  by  add- 
ing other  voices  or  chords.  But  the  moment  we  do 
this,  two  things  happen  simultaneously :  first,  the  har- 
mony is  no  longer  in  one  voice;  second,  personal 
selection  usurps  the  place  of  natural  selection  in  that 
we  add  our  own  thought,  and  thus  transform  some- 
thing that  was  universal  into  something  that  is  per- 
sonal. Hence  the  distinctions  between  natural  and 
personal  harmony,  between  natural  and  personal 
selection.  The  examples  shown  on  page  72  illustrate 
these  distinctions  and  will  suggest  others. 

The  common  and  immutable  forms  at  a)  are  due  to 
natural  selection,  while  the  forms  in  all  the  subsequent 
examples  are  due  to  personal  selection.  Concisely 
stated,  everything  in  more  than  one  voice  is  personal. 
The  harmonic  numbers  in  examples  6),  c),  d)  and 
e)  agree  with  those  in  example  a),  w^hereby  it  is  shown 
that  the  chord-forms  of  personal  selection  may  repro- 
duce and  elaborate  the  original  forms  of  natural  selec- 
tion in  a  variety  of  ways.     Original  harmony  is  there- 


72 


THE  NATURE  OF  MUSIC 


fore  not  only  the  basis  of  chord-harmony,  but  the 
inseparable  bond  between  the  two  is  that  of  feeling  and 
thought,  of  the  simple  and  more  complex,  of  lower  and 
higher  forms  corresponding  to  lower  and  higher  evo- 


a) 


h) 


^^^m^^^ 


e) 


d) 


$ 


^— ^-i 


^==4 


s 


rr^m=^ 


T 


0) 


3    5   13    1     3 


9) 

13     13 


^m 


4^ 


i^ 


f 


^ 


rf=f 


f=f 


^>~i-t-t-f- 


T=P= 


F¥^ 


^ 


^ 


r 


r 


lutionary  states  of  mind.  Not  alone  may  original 
forms  be  reproduced  in  chord-forms,  but  as  seen  in 
examples  /),  g)  and  Z^),^  a  single  melody  may  imply  a 
great  variety  of  other  chord-forms,  and  these  examples 
exhibit  a  more  advanced  state  of  personal  selection 
than  those  which  precede. 

^  Ex.  h)  could  not  be  deciphered.   L.  E.  K. 


DISSONANCE  AND  CONSONANCE  73 

The  eye  and  ear  are  concerned  in  the  following  dis- 
tinction. In  a  written  series  of  single  notes,  as  in 
example  a),  you  can  see  the  notes,  but  you  cannot  see 
the  harmonies,  because  single  notes  present  no  visual 
images  of  harmonic  forms.  Therefore  in  one  voice 
you  are  compelled  to  hear.  With  chords  it  is  different. 
In  a  series  of  written  chords  you  not  only  see  the  notes, 
but  you  can  also  see  the  chords,  because  each  chord 
presents  a  distinct  visual  image  easily  remembered. 
This  explains  why  in  the  study  of  chords  or  harmony, 
as  it  is  called,  students  so  readily  fall  into  the  perni- 
cious habit  of  guidance  by  sight  in  place  of  guidance 
by  hearing.  It  explains  why  most  students  recognize  a 
chord  when  they  see  it,  while  so  few  recognize  a  chord 
when  they  hear  it;  why  most  students  do  their  work 
at  the  piano  and  cannot  hear  what  they  have  written 
unless  they  play  it,  while  so  few  hear  before  they  write 
and  hear  what  they  write  as  they  write.  In  original 
harmony  the  forms  are  invisible;  in  chord-harmony 
they  are  visible.  In  the  former  the  exercise  of  har- 
monic feeling,  perception  and  conception  is  unavoid- 
able and  a  necessity  from  the  start;  in  the  latter  this 
exercise  is  interfered  with,  and  in  most  cases  is  ex- 
cluded by  the  insidious  visual  habit  just  described,  and 
the  necessity  for  this  exercise  is  constantly  urged  upon 
students.  In  the  former  you  cannot  move  one  step 
without  hearing;  in  the  latter,  owing  to  the  visual 
habit,  it  is  possible  to  work  through  an  entire  treatise 
without  hearing.  First  the  idea,  then  the  sign;  first 
hear,  then  write ;  this  subordination  of  symbol  to  idea, 
of  sight  to  hearing,  should  be  a  matter  of  course. 

Original  harmony  and   chord-harmony  are  con- 


74  THE  NATURE  OF  MUSIC 

trasted  in  the  next  examples  for  a  special  purpose. 
In  a)  we  hear  Weber,  in  b)  we  hear  Wagner. 


In  common  parlance  we  would  say  that  these  two 
examples  present  one  and  the  same  melody,  and  that 
b)  is  a  harmonization  of  a).  This  is  not  true.  It 
would  be  true  were  melody  an  element;  it  is  not  true, 
because  melody  is  a  composite  of  two  elements, 
rhythm  and  harmony.  The  two  melodies  look  alike 
but  how  unlike  they  sound.  Are  we  to  believe  the 
eye  or  the  ear  ?  The  harmonic  numbers  indicate  the 
ear's  testimony.  Compare  these  numbers  in  the  two 
examples.  Melodies  are  thoughts.  As  melodies  and 
thoughts,  a)  and  b)  are  distinct;  both  are  equally 
individual  and  natural.  It  is  true  that  a  given  single 
melody  as  at  a)  suggests  a  variety  of  different  har- 
monizations, but  let  us  remember  that  it  is  also  true 
that  every  such  harmonization  results  in  the  trans- 
formation of  one  distinct  and  individual  melody  and 
thought  into  another  distinct  and  individual  melody 
and  thought,  no  two  of  which  can  possibly  be  the  same. 
In  a  separate  chapter  I  will  present  the  potential  har- 
monies of  a  tone,  which  subject  includes  that  of  the 
potential  harmonies  of  a  melody.  Here  it  is  enough 
to  have  pointed  out  the  germinal,  essential  and  indi- 
vidual force  and  character  of  melody  as  thought  both 
spontaneous   and  constructive.     When  a  composer 


DISSONANCE  AND  CONSONANCE  75 

presents  one  or  more  phrases  or  sentences  in  the  form 
of  one  voice,  he  employs  this  form  of  thought  for  purely 
artistic  and  aesthetic  reasons,  the  selection  of  the 
specific  form  of  thought  whether  in  one  or  more 
voices  always  being  personal.  Not  so  with  the  har- 
mony. While  the  composer's  selection  of  one  voice 
is  always  personal,  the  inherent  harmony  of  this  one 
voice  is  never  personal;  it  is  always  original,  univer- 
sal, immutable  harmony.  This  distinction  between 
one-voice  and  multi-voice  harmony  will  appear  in 
other  connections  in  subsequent  sections. 

31.    The  Seven  Original  Tones,     Analysis 

The  seven  original  tones  are  the  components  of  the 
two  harmonic  genera^  consonance  and  dissonance. 
Three  of  the  seven  are  derived  from  the  former,  four 
from  the  latter.  These  seven  tones  are  the  seven  dia- 
tonics  of  the  Major  mode.  Their  minute  analysis 
being  our  immediate  concern,  they  are  again  pre- 
sented. 

13        5.^-^135,       9 

sol  —  ti  —  re  —  fa  —  la 


do  —  mi  —  sol 


Tonic    or    Do  Dominant    or    Sol 

A  harmony  is  named  by  its  root,  hence  the  harmony 
of  the  Tonic  or  Do,  the  harmony  of  the  Dominant  or 
Sol.  The  harmonic  numbers  indicate  either  root  or 
relation  to  root.  These  numbers  are  large  for  major 
and  small  for  minor  intervals.  This  rule  for  marking 
major  and  minor  intervals  will  henceforth  be  strictly 
adhered  to.  Our  example  contains  but  one  minor 
interval,  namely,  /a,  which  is  the  minor  seventh  of 


76  THE  NATURE  OF  MUSIC 

its  root.  The  above  tones  may  be  read  as  follows: 
Tonic-root,  third,  fifth;  Dominant-root,  third,  fifth, 
seventh  and  ninth. 

Every  tone  is  a  distinct  harmonic  percept  and  con- 
cept. A  harmonic  percept  is  our  perception  of  the 
common  report  of  a  tone  as  root  or  third  or  fifth  or 
seventh  or  ninth.  A  harmonic  concept  is  our  thought 
or  conception  of  a  tone  in  any  one  of  these  relations. 
Concepts  are  rooted  in  and  spring  from  percepts  just 
as  percepts  are  rooted  in  and  spring  from  feeling. 
Harmonic  feeling  is  never  wrong,  but  harmonic  per- 
cepts may  be  wrong  and  cause  wrong  concepts.  True 
knowledge  is  true  perception  of  relations.  False  per- 
ception and  consequent  false  conception  is  the  danger 
to  be  averted.  This  danger  is  averted  in  the  present 
study  by  the  common  reports  of  common  feeling  and 
perception.  Since  concepts  are  based  on  percepts, 
since  the  former  are  true  if  the  latter  are  true,  we  will 
for  the  present  fix  our  attention  upon  the  latter. 

The  seven  original  tones  present  eight  distinct  har- 
monic relations,  each  of  which  is  a  harmonic  percept, 
as  follows :  do  is  root,  mi  is  major  third,  sol  is  pure  fifth, 
of  the  Tonic  (harmony  understood);  sol  is  root,  ti  is 
major  third,  re  is  pure  fifth,  fa  is  minor  seventh,  la  is 
major  ninth,  of  the  Dominant.  Of  these  tones  sol, 
the  bond  tone  of  the  two  harmonies,  appears  twice: 
first  as  fifth,  then  as  root. 

Some  of  these  harmonic  percepts  are  original, 
others  are  duplicates.  A  harmonic  percept  is  original 
when  it  is  the  first  of  its  kind:  such  are  do,  the  first 
root;  mi,  the  first  major  third;  sol,  the  first  pure  fifth; 
fa,  the  first  minor  seventh;  la,  the  first  major  ninth. 


DISSONANCE  AND  CONSONANCE 


77 


A  harmonic  percept  is  a  duplicate  when  an  original 
percept  is  repeated  on  another  tone:  such  are  sol  as 
root,  ti  as  major  third,  re  as  pure  fifth.  This  shows 
that  the  seven  tones  and  eight  harmonic  relations  of 
the  two  harmonic  genera,  consonance  and  dissonance, 
have  introduced  ^7;^  original  harmonic  percepts  into 
music.  These  five  are  now  presented  each  with  the 
tone  that  first  produced  it. 

13       5      7      9 

do  —  mi  —  sol  —  fa  —  la  \ 


Three  of  these  spring  from  the  original  consonance 
(Major  Tonic),  two  from  the  original  dissonance 
(Major  Dominant).  The  expansion  of  harmony  and 
tonaHty  is  due  to  the  repetition  of  these  harmonies  and 
percepts  on  other  tones,  a  subject  to  be  treated  in  the 
chapter  on  potential  harmony.  The  exact  analysis 
of  the  above  harmonic  percepts  now  confronts  us. 
These  five  percepts  and  the  seven  original  tones  are 
all  included  in  the  following  simple  folksong  which  we 
will  analyze:  — 


5      3 


3      5     5   3 


5  9 


i: 


S 


m 


i==F^ 


S 


mi       re       re  mi     fa 
Dominant 


mi  fa    sol       mi 
Tonic 


re   la 


5      3^5333     553 


3     3 


I 


k±=£i 


^ — wl-^ 

sol     mi  fa    sol    mi     mi     mi      re     re  mi    fa 
Tonic  Dominant 


-^     -^     -i&- 
ti       ti       do 

Tonic 


78  THE  NATURE  OF  MUSIC 

The  reader  with  a  trained  ear  will  not  stumble  or 
hesitate  over  the  numbers  which  mark  the  harmonic 
relation  of  each  of  the  above  tones;  without  pause  or 
effort  he  at  once  recognizes  E  as  mi  and  major  third 
of  Tonic,  F  as /a  and  minor  seventh  of  Dominant,  G 
as  sol  and  pure  fifth  of  Tonic,  and  so  on.  Through 
practice  he  has  developed  and  transmuted  common 
harmonic  feeling  into  common  harmonic  perception, 
that  is,  true  feeling  of  harmonic  relations  into  true 
perception  of  harmonic  relations,  something  that  he 
once  only  felt  into  something  that  he  now  positively 
knows.  The  result  is  that  he  recognizes  these  rela- 
tions automatically ;  he  not  only  perceives  them  in  the 
concrete  as  in  the  above  melody,  but  he  can  think  of 
them  in  the  abstract  since  in  his  mind  they  have  taken 
shape  as  ideas  and  concepts. 

On  the  other  hand,  the  reader  whose  ear  is  not 
trained  has  all  this  to  learn.  He  may  well  ask :  How 
am  I  to  know  that  the  first  tone  in  this  melody  is  a 
major  third,  that  the  second  is  a  minor  seventh,  and 
so  on  ?  This  analysis  will  at  once  answer  this  ques- 
tion and  explain  harmonic  relations  in  one  voice.  In 
the  succeeding  questions  and  answers  we  will  start 
at  the  bottom. 

What  proof  is  there  that  I  share  in  common  music- 
feeling,  in  a  word,  that  I  am  musical  ?  It  lies  in  the 
fact  that  you  take  pleasure  in  music,  which  in  the 
absence  of  music-feeling  would  not  be  the  case. 

What  proof  is  there  that  my  feeling  of  tone-relation 
is  true  ?  It  lies  in  the  fact  that  you  are  able  to  follow 
and  express  (sing  or  hum)  a  melody  since  each  tone 
in  a  melody  simultaneously  reports  a  definite  relation 


DISSONANCE  AND  CONSONANCE  79 

in  time  (rhythm)  and  a  definite  relation  in  space  (har- 
mony) and  this  double  report  is  the  same  in  all  of  us. 
That  you  feel  this  double  report,  although  you  may  not 
know  what  it  is,  is  proved  by  your  ability  to  follow  and 
express  a  melody.  Feeling  of  melody  is  feeling  of 
united  rhythm  and  harmony,  melody  being  the  com- 
posite of  elements  and  the  original  vehicle  of  music. 

What  proof  is  there  that  each  single  tone  in  a  melody 
is  a  harmony  ?  It  lies  in  the  fact  that  each  tone  arises 
in  the  mind  together  with  elementary  tones  called  con- 
comitants. This  complex  of  a  tone  and  its  concomi- 
tants I  have  already  named  the  harmonic  thread  of  a 
tone.  The  harmonic  thread  of  a  tone  is  the  specific 
harmonic  form  of  a  tone. 

What  causes  the  genesis  in  feeling  of  the  specific 
harmonic  thread  or  form  of  a  tone  ?  The  proximate 
cause  is  the  relation  of  that  tone.  This  form-gener- 
ating relation  inheres  in  and  is  reported  by  melody  in 
each  of  its  tones  and,  as  we  have  seen,  this  relation  is 
at  once  relation  in  time  (rhythm)  and  relation  in  space 
(harmony).  Since  this  relation  is  asserted  in  melody 
it  follows  that  if  you  feel  the  melody  then  do  you  feel 
the  relation  and,  by  implication,  the  harmonic  thread 
or  form  of  each  tone  in  the  melody.  Your  feeling  of 
the  harmonic  thread  of  each  tone  in  the  above  folk- 
song is  true. 

What  course  am  I  to  follow  in  order  to  learn  to 
recognize  and  analyze  these  harmonic  threads  and  so 
transmute  what  I  feel  into  true  perception  and  know- 
ledge.^ Sing  the  first  phrase  of  the  above  folksong 
over  and  over  again  for  the  purpose  of  making  sure 
that  you  retain  the  feeling  of  the  relation  of  the  first 


80  THE  NATURE  OF  MUSIC 

tone  to  the  other  tones  of  the  phrase.  To  retain  the 
feeling  of  the  relation  is  equivalent  to  retaining  the 
feeling  of  the  harmonic  thread  of  their  first  tone,  mi. 
Having  made  sure  of  this  feeling,  sing  mi  and  on  the 
line  of  least  resistance,  drop  on  the  thread  of  har- 
mony from  one  component  to  another  until  you  reach 
a  tone  which  reports  a  stopping-point,  a  point  of  com- 
plete repose,  a  harmonic  centre  of  gravity;  for  this 
tone  is  the  unmistakable  root  or  fundamental  tone  of 
the  thread.  You  will  find  the  harmonic  thread  to  be 
as  follows :  — 

3        15     3      1 


^^ 


mi         do       sol      mi       ffo  =  Root  and  Tonic 

Having  found  the  root,  move  back  on  the  thread  to 
the  tone  you  started  on  and  go  down  and  up  on  the 
thread  repeatedly  as  shown  below :  — 


Once  you  recognize  the  root  then  the  rest  of  the 
analysis  is  simple,  namely,  the  number  and  names  of 
components,  the  interval-relations  of  the  components 
to  the  common  root,  the  proving  of  the  common  root 
not  alone  by  discovering  that  it  is  the  most  stable  of  all 
the  components,  but  by  further  discovering  that  it  is 
the  only  tone  in  the  thread  to  which  the  other  tones 


DISSONANCE  AND  CONSONANCE  81 

relate  in  the  harmonic  order  of  third  and  fifth  in  the  case 
of  this  first  tone  and  as  third,  fifth,  seventh  and  ninth 
in  the  cases  of  other  tones  in  this  folksong.  You  will 
discover  that  in  dropping  on  the  thread  you  passed 
one  root  and  followed  the  thread  to  the  lower  octave 
of  that  root,  that  when  you  pass  a  root  you  repeat 
the  same  series  of  tones  in  a  lower  octave.  In  fine, 
you  have  analyzed  the  harmonic  thread  of  the  first 
tone  (mi)  and  recognize  this  tone  to  be  a  large  or  major 
third  because  it  lies  two  whole  steps  over  its  root. 

As  a  prelude  to  proceeding  with  this  analysis  the 
last  question  and  answer  may  be  given  in  a  briefer 
form.  How  in  one  voice  am  I  to  know  that  a  tone 
is  a  root  or  third  or  fifth  or  seventh  or  ninth  ?  By 
feeling  its  momentary  relation  and  analyzing  its  har- 
monic thread. 

Second  tone  fa,  minor  seventh.  The  harmonic 
thread  of  this  tone  hsisfour  components;  its  root  is  the 
Dominant.  This  thread  is  given  at  a)  followed  by  an 
exercise  at  6). 

a)  b) 

,       5    3    1  ,531 


h-f/^       h'  ujiJ^ 


fa         re      ti     sol— root  or  Dominant  fa  sol 

Third  tone  sol,  pure  fifth.     Its  analysis  follows. 
0  h) 

5         3        1  5       3      1 


i 


m 


sol  mi        do  =root  or  Tonic  sol  do 


82  THE  NATURE  OF  MUSIC 

The  next  three  tones  are  repetitions  of  the  first, 
namely,  mi,  major  third. 

Seventh  tone  re,  pure  fifth  of  the  Dominant.  This 
time  the  Dominant-thread  reports  but  three  compo- 
nents. 

a)  6) 

5         3       1  .531 


^- ""=^-|-j    i~TT^ 


r    J  ^  r    »  j  » 

re  ti  sol  =  root  or  Dominant      re  sol 

The  next  five  tones  are  repetitions  of  percepts  already 
analyzed. 

Thirteenth  tone  la,  major  ninth  of  Dominant. 
This  time  the  Dominant-thread  reports  five  compo- 
nents. 

a) 

9^531 


i 


-^ 


rrfW 

la      fa     re     ti     «>/= Dominant  la  tci 

Excepting  the  last  two  all  the  remaining  tones  are 
repetitions  of  those  already  analyzed. 

Last  tone  hut  one,  ti,  major  third  of  Dominant. 
On  ti  as  on  re  the  Dominant-thread  reports  three 
components. 

a)  h) 

3153    1  31531  31 

J 


W^t.: L^rr.rrfl^M 


^&^i^ 


ti    sol  re  ti  «oZ= Dominant  ii  sol 


DISSONANCE  AND  CONSONANCE  83 

Last  tone  do,  the  Tonic,  root  of  Tonic-harmony, 
the  genus  consonance  and  music's  first  regnant  har- 
mony. 

a)  b) 

1531153  1351 


f^^^i^r^i^ij 


3^ 


do      sol    mi    do        do  do  do  do  do 

Here  ends  the  analysis  of  the  common  report  of  the 
harmonic  relation  and  form  of  each  individual  tone 
in  this  melody.  However,  the  harmonic  analysis  is 
not  yet  complete.  As  we  sing  and  think  over  this 
melody  we  observe  in  addition  to  the  fact  that  each 
tone  reports  a  harmony  another  fact,  namely,  that 
certain  rhythmic  groups  of  these  tones  relate  to  and 
report  the  predominance  of  a  specific  harmony,  which 
I  have  already  named  the  regnant  harmony.  Thus 
in  each  small  phrase  we  observe  a  change  from  one 
regnant  harmony  to  another,  now  the  Tonic,  now 
the  Dominant,  as  marked  in  the  example.  Thus  the 
first  small  phrase  changes  from  Tonic  to  Dominant, 
the  second  from  Dominant  to  Tonic,  and  so  on.  Reg- 
nant harmony  being  the  special  subject  of  the  next 
chapter  w^e  need  pause  here  only  for  a  few  observa- 
tions. We  note  that  these  changes  of  harmony  are 
instantaneous  and  recurrent;  hence  the  implication 
of  rhythm  in  causing  these  changes.  So  far  I  have 
accounted  for  the  genesis  of  but  one  regnant  har- 
mony, the  Tonic,  since  every  conceivable  succession 
of  Tonic-components  generates  the  Tonic-harmony 


84 


THE  NATURE  OF  MUSIC 


and  cannot  possibly  generate  any  other  harmony. 
The  answer  in  the  next  chapter  to  the  question  How 
did  a  second  regnant  harmony  arise?  becomes  in- 
creasingly important.  Sol,  originally  fifth  of  Tonic, 
could  not  appear  as  a  root  until  the  regnant  Domi- 
nant-harmony had  been  generated.  In  passing  let  us 
observe  that  the  Tonic-harmony,  whether  represented 
by  do  or  mi  or  sol,  is  always  a  three-tone  thread.  A 
review  of  the  foregoing  analysis  will  show  on  the  other 
hand  that  the  Dominant-harmony  is  a  three-tone 
thread  on  ti  and  re,  sl  four-tone  thread  on  fa,  a  five- 
tone  thread  on  la.  From  these  threads  of  three,  four 
and  five  tones  are  derived  the  chords  composed  of 
corresponding  numbers  of  tones  and  known  as  the 
Tonic -triad,  the  Dominant  -  triad,  the  Dominant- 
seventh  chord  and  the  chord  of  the  major  ninth,  in  all 
their  forms  and  positions. 

While  the  regnant  Dominant  appears  in  the  above 
folksong  the  tone  sol  does  not  appear  in  it  as  a  root. 
The  following  melody  is  selected  because  it  presents 
sol  as  root.  In  fact,  it  presents  the  five  original  per- 
cepts, and  the  seven  original  tones  in  their  eight  rela- 
tions to  the  Tonic  and  Dominant. 


3      ^351391 


1^3511     6 


i 


y   r^      r  f  » 


^ 


a 


I 


^3 


^ 


mi     fa  mi  re  do    ti     la      sol      fa      sd  fa  mire   do    do    sd 
Tonic  Dominant.  Tonic. 


This  analysis  suffices   to  establish  the  following 
theses  as  scientific  truths. 


DISSONANCE  AND  CONSONANCE  85 

1.  Original  harmony  is  harmony  in  one  voice  and 
the  harmonic  basis  of  music. 

2.  The  original  dissonance  and  consonance  had 
their  genesis  in  one  voice,  and  their  component  tones 
are  the  seven  original  tones  here  identified  as  the  seven 
diatonics  of  the  Major  mode. 

3.  Harmony  in  one  voice  asserts  itself;  each  indi- 
vidual tone  reports  itself  as  root  or  third  or  fifth  or 
seventh  or  ninth,  and  these  reports  are  common  and 
unalterable. 

4.  Rhythmic  groups  of  tones  generate  and  assert 
their  relation  to  a  particular  subharmony ;  now  it  is  one 
regnant  harmony,  now  it  changes  to  another  regnant 
harmony.  In  one-voice  music  the  regnant  harmonies 
arise  by  natural  selection,  in  multi-voice  music  they 
are  due  to  personal  selection.  Regnant  harmony  de- 
termines the  exact  relation  of  each  tone  in  a  melody. 

5.  From  the  original  dissonance  and  consonance 
are  derived  three  fundamental  forms  of  harmony, 
namely,  the  three-tone,  four-tone  and  five-tone  forms ; 
five  original  harmonic  percepts,  namely,  1,  3,  5,  ?,  9. 

6.  The  mode-idea  had  its  origin  in  the  basic  rela- 
tion of  cadence  and  repose,m  which  relation  the  original 
dissonance  and  consonance  had  their  origin.  From 
the  first  the  mode  has  been  harmonic  and  is  based  on 
the  two  harmonic  genera  of  tones.  The  tones  of  the 
two  genera  being  the  seven  Major  diatonics  it  follows 
that  the  Major  mode  is  the  original  mode. 

7.  Melody  is  the  composite  vehicle  which  has  intro- 
duced one  by  one  all  these  tones,  percepts,  forms  and 
regnant  harmonies  of  the  Major  mode. 

The  harmonic  reports  given  in  the  above  analyses 


S6  THE  NATURE  OF  MUSIC 

cannot  be  changed,  not  by  tempo,  slow  or  fast;  not 
by  dynamics,  loud  or  soft;  not  by  interpretation, 
legato  or  staccato  ;  they  are  what  they  are,  not  by  man's 
will,  but  by  the  universal  will  and  immutable  laws 
inherent  in  tone-rhythmic  relation.  The  prevalent 
chord-conception  of  harmony  is  responsible  for  the 
distinction  between  harmonic  tones  and  melodic  tones ; 
the  component  tones  of  a  "presiding  chord"  being 
called  harmonic  while  the  tones  that  lie  over  and  under 
and  play  upon  the  chord-tones  are  called  melodic. 
This  distinction  has  lost  its  usefulness  since  it  has  been 
demonstrated  that  each  individual  tone,  whether  it 
belongs  to  the  "presiding  chord"  or  not,  is  harmonic. 
Were  this  not  true  there  would  be  and  could  be  neither 
tone-cadence  nor  tone-repose,  neither  dissonance  nor 
consonance,  no  relation  in  the  musical  sense,  in  short, 
no  music.  The  truth  that  every  tone  is  harmonic  is 
here  based  on  the  testimony  of  the  inner  ear  which  is 
the  testimony  of  common  feeling  and  perception.  This 
truth  is  reported  in  all  music,  primitive  and  artistic, 
before  Bach,  of  Bach,  after  Bach. 

32.    On  Symbols 

The  symbols  thus  far  employed  are  notes,  syllables 
and  harmonic  numbers.  To  these  we  will  add  scale- 
numbers,  for  which  purpose  the  seven  original  tones 
are  now  presented  in  the  familiar  form  of  the  Major 
scale. 

15     3^      59or33     1 


—y ■■ 

"~7 

-- 

Cy 

II 

fc\ 

^ 

^ 

f^ 

11 

Vs} 

^ 

II 

%J 

-&- 

25>~ 

do 

re 

mi 

fa 

sol 

la 

ti 

do 

1 

2 

3 

4 

5 

6 

7 

8 

DISSONANCE  AND  CONSONANCE  87 

Here  the  syllables  indicate  the  mode-tones;  the 
notes,  the  pitch  or  key  of  the  mode-tones;  the  upper 
row  of  numbers,  the  inherent  harmonic  relations ;  the 
lower  row  of  numbers,  the  scale-order  from  the  first 
to  the  eighth  tone.  Scale-numbers  are  outside,  not 
inside  numbers.  Street-door  numbers  tell  us  nothing 
of  what  is  going  on  inside  of  a  house ;  no  more  do  scale- 
numbers  tell  us  what  is  going  on  inside  of  a  tone ;  that 
is,  they  give  us  no  intelligence  whatever  of  the  inherent 
harmonic  relations  of  tones.  To  be  sure  the  scale- 
numbers  1,  3,  5  happen  to  correspond  with  the  har- 
monic numbers  over  do^  mi  and  sol,  but  the  fact  that 
we  know  that  re,  /a,  la  and  ti  are  respectively  the 
second,  fourth,  sixth  and  seventh  tones  of  the  scale 
by  no  means  implies  the  slightest  knowledge  of  the  one 
thing  we  should  know,  namely,  the  inherent  harmonic 
relations  of  the  tones.  We  have  seen  that  during  the 
regnancy  of  the  Tonic,  re  is  5,  fa  is  7,  la  is  3,  <i  is  3 ; 
that  during  the  regnancy  of  the  Dominant,  the  rela- 
tions of  these  tones  are  the  same  except  in  the  case  of 
/a,  which  is  a  ninth.  There  are  no  harmonic  percepts 
answering  to  the  scale-numbers  2,  4  and  6.  The  habit 
of  orientation  by  means  of  scale-numbers  is  so  fixed 
that  when  students  begin  the  study  of  one-voice  har- 
mony they  are  very  apt  to  confuse  the  scale-numbers 
with  the  harmonic  numbers  and  vice  versa.  Scale- 
numbers  serve  a  useful  purpose,  but  that  purpose 
should  be  defined.  We  will  define  all  the  above  sym- 
bols and  so  avoid  the  confusion  which  would  otherwise 
be  inevitable. 

1.  A  note  with  and  without  modifying  sharp,  flat  or 
natural,  is  the  sign  and  index  of  the  relative  pitch  of  a 


88  THE  NATURE  OF  MUSIC 

tone.    This  defines  the  note  according  to  its  position 
on  the  staff. 

The  metrical  shape  of  a  note  is  the  sign  and  index 
of  the  relative  length  of  the  rhythmic  period  of  a  tone. 

2.  A  syllable  is  the  sign  and  index  of  the  mode- 
relation  of  a  tone.  By  means  of  the  syllables  we  are 
able  to  think  and  express  the  mode-relations  without 
any  connection  with  fixed  pitch  or  key.  But  the  terms 
mode-relation  and  key-relation  become  synonymous 
the  moment  the  mode-relations  are  pitched  or  keyed 
in  staff-notation.  C  Major  means  (fo-Major  pitched 
or  keyed  on  C,  but  Major  always  is  c?o-Major  whatever 
be  the  pitch  or  key  of  mode. 

3.  A  harmonic  number  is  the  sign  and  index  of  the 
inherent  harmonic  relation  of  a  tone. 

4.  A  scale-number  is  the  sign  and  index  of  the  rela- 
tive position  of  a  tone  in  a  scale.  In  the  Roman  form 
these  numbers  are  employed  as  indices  of  the  sub- 
harmonies,  that  is,  of  regnant  harmonies.  Thus,  for 
example,  the  Tonic  is  marked  I,  the  Dominant  is 
marked  V,  the  two  roots  being  the  first  and  fifth  tones 
of  the  scale. 

Of  all  these  signs  the  harmonic  numbers  are  the 
most  important.  Through  the  discovery  of  original 
harmony  in  one  voice  these  harmonic  numbers  have 
gained  a  theoretic  and  practical  value  which  hitherto 
they  have  not  possessed.  Their  report  in  one  voice  is 
exact,  synthetic  and  complete:  exact,  because  their 
harmonic  report  is  the  common  report  of  common 
feeling  and  perception ;  synthetic,  because  their  exact 
report  of  inherent  harmonic  relation  includes  the  feel- 
ing and  idea  of  mode,  key  and  interval;  complete. 


DISSONANCE  AND  CONSONANCE  89 

because  their  exact  and  synthetic  reports  are  indis- 
solubly  associated  with  rhythm,  and  therefore  embody 
the  complete  intelligence  of  a  tone's  relation.  This 
harmonic  report  of  a  tone's  relation  is  therefore  the 
essential  and  fundamental  thing  to  observe,  name  and 
know. 

33.    The  Five  Components  of  Harmony 

There  are  hut  Jive  components  of  harmony,  namely, 
root,  third,  fifth,  seventh,  ninth.  The  truth  of  this 
generalization  is  in  no  way  impaired  by  the  fact  that 
there  are  numerous  modified  forms  of  these  five. 
Some  harmonies  have  three,  some  four,  some  five  com- 
ponents, but  none  exceed  the  number  oi  Jive.  The 
ninth  is  the  genetic  limit  oj  harmony.  Common  har- 
monic feeling  and  perception  report  and  admit  no 
harmonic  components  beyond  the  ninth.  Root,  third, 
fifth,  seventh  and  ninth,  being  the  only  harmonic  per- 
cepts, they  are  the  only  harmonic  components.  Chord- 
theories  have  admitted  elevenths  and  thirteenths  as 
components  of  chords  and  therefore  as  components  of 
harmony.  Such  elevenths  and  thirteenths  are  purely 
theoretical  concepts,  which  are  as  false  as  they  are 
arbitrary  since  they  have  no  foundation  in  and  are 
confuted  by  common  feeling  and  perception.  On 
page  90  will  be  found  two  examples  which  present 
these  elevenths  and  thirteenths  in  their  true  light  as 
arbitrary  computations  of  intervals  from  a  given  root 
which  at  a)  is  the  Tonic  and  at  h)  is  the  Dominant. 

The  lower  row  of  numbers  in  both  examples  indi- 
cates the  arbitrary  chord-intervals  from  1  to  13.  The 
upper  row  of  numbers  in  both  examples  is  the  true 


90  THE  NATURE  OF  MUSIC 

index  of  the  common  harmonic  report  of  each  tone  in 
correlation  with  all  the  other  tones.  Compare  the 
two  sets  of  numbers.  In  a)  the  chord-intervals  7,  9, 
11  and  13  are  respectively  3,  5,  ?  and  9,  which  are 
components  of  the  Dominant.  In  h)  the  chord-inter- 
vals 11  and  13  are  respectively  1  and  3  of  the  Tonic. 
The  large  notes  in  both  examples  show  that  both  of 
these  chords  combine  components  of'  two  harmonies ; 
each  contains  two  roots. 

a)      13  5-135^9 


k± 


i) 


1     3    5      7    9  11    13 
1      3    5,91      3 


i 


i 


1      3    5    7    9   11     13 

Chords  formed  by  combining  the  component  tones 
of  one  harmony  I  name  simple  chords ;  such,  for  exam- 
ple, are  all  the  forms  of  the  major  triad.  Chords,  like 
those  in  the  above  examples,  which  are  formed  by  com- 
bining the  component  tones  of  two  or  more  harmonies, 
I  name  compound  chords. 

Tones  which  relate  to  but  one  root  I  name  simple 
harmonics;  such  are  1,  3,  5  of  the  Tonic  and  1,  3,  5, 
7,  9  of  the  Dominant.  Tones,  like  sol  in  example  a), 
which  simultaneously  relate  to  two  roots  I  name  com^ 
pound  harmonics. 

Simple  and  compound  chords  and  harmonics  are 


DISSONANCE  AND  CONSONANCE  91 

subjects  to  be  treated  later  on.  Meanwhile  the 
above  examples  clearly  point  out  the  necessity  for 
making  careful  distinctions  between  harmonic  com- 
ponents which  never  exceed  the  number  of  five  and 
chord-components  which  are  not  limited;  between  har- 
monic intervals  and  chord-intervals;  between  har- 
monic concepts,  supported  and  verified  by  common 
feeling  and  perception,  and  chord-concepts,  which  the 
common  reports  prove  to  be  false,  and  which  therefore 
are  arbitrary,  misleading  and  untenable. 

34.    The  Five  Original  Cadences.     Mode  Defined 

The  relation  of  cadence  and  repose  is  the  basis 
of  mode.  The  relation  of  tone-cadence  and  tone- 
repose  originated  in  the  relation  of  one  harmony  (dis- 
sonance) to  another  harmony  (consonance).  This 
inter-harmonic  relation  is  mode-relation.  The  pre- 
ceding account  of  the  origin  and  nature  of  original 
dissonance  and  consonance  in  one  voice  is  equivalent 
to  an  account  of  the  origin  and  nature  of  the  Major 
mode.  The  original  mode  is  Major  because  the  ori- 
ginal consonance  is  major.  The  aggregate  relations 
of  the  two  harmonic  genera  may  be  called  briefly  the 
major  consonance  and  its  cadences. 

Melody  has  brought  forth  two  modes :  first,  the  Major 
mode  based  on  the  major  consonance  and  its  cadences ; 
second,  the  Minor  mode  based  on  the  minor  conso- 
nance and  its  cadences.  The  origin  of  the  former  has 
been  explained;  the  origin  of  the  latter  is  the  subject 
of  a  later  chapter.  In  mode-parlance  what  has  just 
been  called  the  major  consonance  and  its  cadences 
is  the  Major  Tonic  (-harmony)  and  its  cadences. 


9«  THE  NATURE  OF  MUSIC 

Three  marks  succinctly  symbolize  the  mode-idea  as 
follows :  — 


In  the  above  order  these  marks  signify  rising  ca- 
dence, falling  cadence,  repose.  Join  these  marks  and 
we  form  a  simple  sign  for  the  Major  mode,  thus :  — 


The  Major  Tonic  and  its  cadences  are  the  five  origi- 
nal cadences  of  music.  They  are  given  below  where 
each  tone  is  numbered  according  to  its  genus-relsition. 

I      3 
o)3     1515      3,      395  6)  3       1 


ti      do       re     do      re      mi      fa      mi      la       sol 


:|^ 


In  a)  the  cadences  are  single,  in  b)  they  are  com- 
bined in  chords.  Ti  resolves  in  an  upward  half  step, 
fa  in  a  downward  half  step :  I  therefore  name  ti  the 
upleader,  fa  the  downleader.  Of  the  original  four 
cadence-tones  re  is  the  only  one  that  reports  both  a 
rising  and  a  falling  cadence ;  in  both  of  its  cadences  re 
resolves  in  a  whole  step.  La  reports  its  falling  cadence 
by  resolving  in  a  downward  whole  step.  Of  these 
five  original  cadences  two  are  rising,  three  are  falling, 
two  resolve  in  half  steps,  three  in  whole  steps. 

Although  we  may  be  able  to  hear  these  whole  and 


DISSONANCE  AND  CONSONANCE  93 

half  steps  and  able  to  name  the  two  tones  in  each, 
although  we  may  be  able  to  perceive  and  name  all 
intervals  from  primes  to  elevenths  and  able  to  define 
tjiem  as  pure,  major,  minor,  augmented  and  dimin- 
ished, double-augmented  and  double-diminished,  yet 
at  the  same  time  we  may  have  no  perception  and  may 
be  completely  ignorant  of  the  one  thing  essential  to 
our  intelligent  and  true  appreciation  of  a  step  and  an 
interval,  namely,  the  inherent  harmony  of  each  of  the 
two  tones  that  form  a  step  and  interval.  For  exam- 
ple. Besides  hearing  that  the  two  tones  in  the  first 
of  the  above  cadences  are  ti  and  do  and  that  the  step 
is  a  half  step  and  an  upward  resolution,  you  should 
hear  that  you  are  stepping  from  the  third  of  one  har- 
mony (Dominant)  to  the  root  of  another  harmony 
(Tonic).  The  perception  of  these  harmonic  and 
inter-harmonic  relations  is  imperative.  Far  from  in- 
veighing against  the  customary  study  and  practice  of 
intervals,  I  consider  the  working  out  of  intervals  from 
each  tone  in  the  octave  both  a  necessary  discipline 
and  an  essential  part  of  every  student's  mental  equip- 
ment and  technique.  But  students  are  warned  to  dis- 
criminate with  care  between  interval-numbers  which 
indicate  the  distance  from  one  tone  to  another  and 
harmonic  numbers  which  indicate  the  harmonic  rela- 
tion of  each  individual  tone  to  its  root. 

There  being  no  melody  apart  from  mode  each 
tone  in  a  melody  is  a  mode-tone.  There  are  three 
groups  of  mode-tones :  1.  Diatonics.  2.  Chromatics. 
3.  Enharmonics.  We  have  seen  that  tone  connotes 
harmonic  form  and  harmonic  relation,  and  that  a 
specific  form  is   due  to  a  specific  relation.     There- 


94  THE  NATURE  OF  MUSIC 

fore  these  three  groups  of  mode-tones  are  three 
groups  of  mode-relations.  Both  mode  and  tonality 
mean  tone-relation,  and  at  one  time  the  two  terms 
were  synonymous.  The  evolutionary  expansion  qf 
tonality  consequent  on  the  development  of  modern 
music  has  changed  all  this.  While  tonality  compre- 
hends all  that  is  mode,  mode  does  not  comprehend  all 
that  is  tonality.  Definitions  will  explain.  The  mode 
is  the  sum  of  relations  in  one  key.  Tonality  is  the 
sum  of  relations  in  all  keys.  The  mode  is  concerned 
with  the  interharmonic  relations  of  one  key,  tonality 
with  the  interharmonic  relations  of  all  keys.  Thus 
tonality  is  a  general  term  and  comprehends  all  that  is 
mode.  The  evolution  of  the  mode  is  therefore  the 
first  chapter  in  the  evolution  of  tonality:  the  three 
groups  of  tones  and  relations  are  three  evolutionary 
stages  of  tonality.  The  first  stage  culminated  in  the 
completion  of  the  foundation-group  of  seven  diatonics, 
which  is  the  subject  still  before  us.  We  have  symbol- 
ized and  named  each  of  these  tones  by  a  syllable,  a 
note  in  the  key  of  C,  and  a  scale-number.  Each  is 
also  known  by  a  technical  name  which  is  added  to  the 
other  names  in  this  example. 

Tonic      Super-  Mediant      Sub-  Dominant     Sub-  Subtonic    Tonic 
tonic  dominant  mediant 


L/ ■■                                                       - -- -                                 n 

/f                                                                                                ^            a        M 

fc\ 

a 

O' 

■  n 

\s) 

a> 

11 

do 

I 

re 

n 

mi 

III 

fa 

IV 

ad 
V 

la 

VI 

a 
VII 

<fo 
I 

The  unity  of  the  mode-idea  is  exemplified  by  all 
these  symbols  except  the  notes  which  fix  the  pitch  or 
key  of  mode  on  C. 


DISSONANCE  AND  CONSONANCE  95 

Original  harmonic  forms  and  relations  are  the  pro- 
totypes of  all  like  forms  and  relations.  Such  proto- 
types are  the  major  consonance,  the  four-tone  and 
five-tone  dissonance,  the  Major  mode,  the  five  original 
percepts  1,  3,  5,  ?,  9,  the  upleader  ti,  the  downleader 
fa.  We  shall  see  that  the  evolutionary  expansion  of 
tonality  and  of  the  tone-system  are  due  on  the  one 
hand  to  the  multiplication  of  these  prototypes,  on  the 
other  hand  to  the  production  of  new  types  which  in 
their  turn  are  multiplied.  The  multiplication  of  exist- 
ing types  will  be  explained  by  the  psychological  prin- 
ciple that  all  forms  and  relations  in  experience  are 
potential  in  and  pitchable  ^  on  all  tones  in  experience. 
The  production  of  new  types  will  be  explained  by  the 
psychological  principle  of  tone-genesis,  the  eflficient 
accent.  Meanwhile  the  relation  of  tonality  and  tone- 
system  requires  definition.  The  tone-system  is  the 
index  and  scale  of  tones  in  use.  The  tones  had  their 
origin  in  relation,  therefore,  in  tonality.  Tonality  and 
tone-system  therefore  stand  in  the  relation  of  cause 
and  consequence.  The  development  of  the  latter  was 
dependent  on  and  concurrent  with  that  of  the  former. 
The  diatonic  stage  of  tonality  caused  the  diatonic  divi- 
sion of  the  octave  which  resulted  in  the  diatonic  scale- 
system.  The  chromatic  stage  of  tonality  caused  the 
chromatic  division  of  the  octave  which  resulted  in  the 
chromatic  scale-system.  The  enharmonic  stage  of 
tonality  caused  the  enharmonic  division  of  the  octave 
which  resulted  in  our  modern  enharmonic  scale-sys- 
tem. This  division  of  the  octave  is  due  to  tonality, 
not  to  equal  temperament  as  physicists  believe.    Tem- 

^  Reading  uncertain.    L.  E.  K. 


96 


THE  NATURE  OF  MUSIC 


perament  there  is  in  musical  instruments  like  the 
piano,  but  in  music  itself  there  is  no  temperament.  A 
piano  is  tempered  for  the  purpose  of  meeting  psycho- 
logical not  physical  requirements;  to  temper  a  piano 
is  to  shape  physical  means  to  psychological  ends. 
Tonality  is  a  question  of  psychology,  not  of  physics. 
No  two  half  steps,  no  two  whole  steps,  no  two  intervals 
of  any  denomination,  have  exactly  the  same  length. 
The  cause  lies  in  tonality,  which  is  a  web  of  harmonic 
threads.  In  evolution  thread  upon  thread  has  been 
added  to  this  web,  so  that  at  the  present  time  the 
meshes  of  its  thousand  threads  are  so  fine  and  delicate 
that  they  almost  co^iceal  the  diatonic  ^^ni^^-threads  with 
the  result  that  some  theorists  have  denied  the  existence 
of  such  a  thing  as  mode  or  key.  Two  simple  exer- 
cises will  fix  the  two  gr^/ii/^-threads  which  comprise  the 
seven  diatonics,  in  the  mind  of  the  student. 


a) 


3    5 


b) 


ti    re    fa     la    sol  mi  do 

V  I 


la    fa     re     ti 

V 


do   mi    sol 
I 


35.   Progression  and  Resolution 

Steps  from  tone  to  tone  are  either  progressions  or 
resolutions.  The  step  from  a  cadence-tone  to  a  re- 
pose-tone is  a  resolution  on  the  line  of  least  resistance. 
Every  step  not  a  resolution  is  a  progression.  Every 
step  being  either  the  one  or  the  other  of  the  two  the 
distinction  between  the  two  is  very  important.     Since 


DISSONANCE  AND  CONSONANCE 


97 


tones  are  either  in  cadence  or  repose  we  proceed  from 
tone  to  tone  in  four  ways  as  follows :  — 

1.  From  cadence  to  repose      =  resolution. 

2.  From  repose  to  cadence      =  progression. 

3.  From  cadence  to  cadence  =  progression. 

4.  From  repose  to  repose        =  progression. 

These  four  species  of  steps  appear  in  the  next  exam- 
ple: cad.  and  rep.  indicate  respectively  cadence-tone 
and  repose-tone :  the  slurs  indicate  resolutions,  and  all 
the  other  steps  are  progressions. 


1 

do 


3      1 

H       do 


re 


5 

sol 


1 

do 


m 


i 


* 


rep.      cad.     rep.       cad.       rep.      rep.      cad.      cad.       rep. 

In  the  following  ascending  and  descending  scales 
each  progression  and  resolution  is  marked  pro.  and 
res.  respectively.  There  are  two  rising  cadences  or 
resolutions  in  ascending  and  three  falling  cadences  or 
resolutions  in  descending.  The  step  from  fa  up  to 
sol  at  N.B.,  although  it  proceeds  from  a  cadence-tone 


a) 


15    3     7N.B.  5     3    3     1 


i^  !  ij 


pro.    res.  pro.     pro.    pro.  pro.   res. 


mi 


h) 


1335        1351 


i^ 


1 — I — [ 


■^T^ 


m 


pro.  pro.    res.      pro.    res.    pro.  res. 


98  THE  NATURE  OF  MUSIC 

to  a  repose-tone,  is  a  progression,  because  the  cadence 
of /a  falls  to  mi  and  does  not  rise  to  soL  All  such 
evasions  of  the  inherent  cadence  of  a  tone  are  classed 
as  progressions. 

The  moment  a  series  of  tones  is  thought  rhythmi- 
cally it  at  once  becomes  melody  and  asserts  its  inherent 
regnant  harmony,  which  in  both  of  the  above  examples 
is  the  Tonic. 

In  a  former  writing  ["  The  Septonate  "]  I  misnamed 
progression  by  calling  it  a  principle.  Progression  is 
neither  a  cause  nor  a  principle.  The  same  is  equally 
true  of  resolution.  Both  progression  and  resolution 
are  effects  of  causes  inherent  in  the  rhythmo-harmonic 
relation  of  the  two  tones  forming  a  specific  step. 

From  rhythm  we  have  derived  the  basic  relation  of 
cadence  and  repose.  In  their  application  to  tone  the 
terms  cadence  and  repose  have  thus  far  been  used  in 
exclusive  connection  with  the  four  original  cadence- 
tones  {ti,  re,  fa,  la)  and  the  three  repose- tones  (do,  mi, 
sol),  in  short,  with  the  Major  Tonic-harmony  and  its 
cadences.  From  this  their  original  and  restricted 
sense  we  are  presently  to  use  these  terms  in  a  wide  and 
general  sense  as  applying  to  tone-relation  in  general. 
Since  every  tone  may  appear  in  cadence  or  repose  it 
follows  that  this  basic  relation  derived  from  rhythm 
and  then  connected  with  specific  tones  will  henceforth 
apply  to  tones  and  tone-relations  in  general. 

36.    A  First  Music-Lesson 

The  material  to  be  presented  is  as  follows :  — 
1.  Rhythm :  simple  dual  and  triple.     2.   Harmony: 
the    Major  Tonic    and   its  five  diatonic    cadences. 


DISSONANCE  AND  CONSONANCE  99 

Method  to  proceed  from  generals  to  particulars,  from 
perception  to  conception. 

The  purpose  of  a  first  lesson  is  to  transmute  a 
child's  latent  feeling  of  the  inherent  rhythm  and 
harmony  of  melody  into  accurate  observation.  Pre- 
sent a  simple  diatonic  melody  and  point  out  its  rhythm 
and  harmony  in  a  general  way,  leaving  particulars  for 
the  last  part  of  lesson.  Next  present  and  explain  ma- 
terial as  follows:  — 

1.  Rhythm:  dual  and  triple  forms:  light  and 
heavy  accents:  relation  of  these  alternating  accents 
to  form,  to  keeping  time  and  balance :  no  rhythm,  no 
form :  rhythm  the  foundation  of  form.  Let  the  child 
express  rhythm:  beat  it,  walk  it,  talk  it,  as  follows:  — 

Simple  Dual  Forms. 

a)  light  heavy)  b)  heavy  light)  ^ 

now  now    )    '^  now    now)    ^ 

Simple  Triple  Forms, 

a)  light  light  heavy )  ^^  h)  light  heavy  light )  j.       ^ 

now  now  now    )  now  now     now)     *^ 

c)  heavy  light  light) 
now     now  now) 

Select  words  whose  relative  accents  correspond  with 
all  these  forms. 

2.  Harmony:  Let  the  student  learn  first  the  three 
repose-tones  of  the  Tonic,  their  syllables  and  harmonic 
numbers ;  next,  the  four  cadence-tones,  their  syllables 
and  harmonic  numbers;  next  the  five  diatonic  ca- 
dences. Observe  that  the  repose-tones  and  cadence- 
tones  each  combine  in  a  harmony  and  chord  and 
resolve    the    cadence-chord    into    the    repose-chord. 


100  THE  NATURE  OF  MUSIC 

This  is  the  harmonic  foundation,  it  is  all  in  you. 
Observe  and  verify  it  in  yourself  and  others.  Hear  it, 
feel  it;  name  it,  think  it;  sing  it,  play  it;  read  it,  write 
it,  and,  as  a  child  of  six  once  prompted  me,  **then 
know  it." 

3.  Now  return  to  the  simple  melody  with  which 
you  started.  Define  its  rhythm,  name  each  of  its 
tones  by  a  syllable,  point  out  each  cadence-tone  and 
repose-tone  and  give  each  its  harmonic  number  indi- 
cating its  harmonic  relation. 

For  many  years  I  have  given  this  first  lesson  to 
students  of  all  ages.  If  desirable  the  above  material 
may  be  divided  so  as  to  occupy  two  or  three  lessons. 
To  learn  the  lesson  and  learn  it  thoroughly  is  impor- 
tant ;  how  long  it  takes  to  accomplish  this  is  unim- 
portant. Study  music  and  be  a  musician.  Music 
is  the  what ;  technique  is  the  how.  The  latter  equals 
zero  if  not  based  on  the  former.  The  musician  has 
something  to  say;  he  has  the  right  to  speak  and  be 
heard;  his  technique  is  a  means  to  an  end;  his  art  is 
music.  On  the  other  hand,  the  mere  technician  has 
nothing  to  say;  he  has  no  such  right;  his  astounding 
technique  amounts  to  an  astounding  facility  in  saying 
nothing;  what  should  be  a  means  becomes  an  end  in 
itself;  his  art  is  mechanism;  his  expression  is  jejune 
jingle.  It  is  never  too  late  to  learn  a  first  music- 
lesson. 


DISSONANCE  AND  COIs^SOMNCE'  lOV 


37.    Work  for  Students 

Work  and  write  out  the  following  material  in  all 
keys,  namely,  in  C,  G,  D,  A,  E,  B,  FJ^,  Cjj: ;  in  F,  BK  EK 
Al7,  DK  GP,  Ct;. 

Consonance  Dissonance  Resolution 

13         5         3      5,9 


i 


_^5-/« 1 


f 


do 

I 


mi 


•U 


a 
V 


fa        la 


V     I 


i 


Two  Rising  Cadences 


Three  Falling  Cadences 


-g ^ 


^^j 


n,^       '     '^ 


-&-  ■'>— / 


-(S?- 


Additional  work  for  students  will  be  indicated  from 
time  to  time  as  we  proceed. 


CHAPTER   IV 

THE  EFFICIENT  ACCENT  AND  REGNANT  HARMONY 
OF  MELODY 

38.    Regnant  Harmony  in  One  Voice  and  Its 
Principle  of  Genesis  Explained 

In  preceding  chapters  we  have  traced  the  genesis 
of  harmony  back  to  music  in  one  voice  or  homophony. 
In  the  chapters  before  us  we  are  to  trace  the  evolution 
of  homophonic  harmony  in  a  sequence  of  cause  and 
effect.  Through  the  sudden  transference  of  the  har- 
monic basis  of  music  from  the  chord  to  homophony, 
through  the  consequent  lengthening  of  the  age  of 
harmony  from  a  period  of  evolution  extending  over 
but  a  few  centuries  of  chords  to  a  period  reaching 
back  from  the  present  to  the  first  beginnings  of  music 
unknown  ages  ago,  in  short,  through  the  discovery  of 
original  harmony  in  one  voice  and  its  common  reports, 
the  subject  of  homophony  suddenly  stands  forth  in 
a  new  light  and  gains  a  new  theoretic  and  historic 
significance  and  prominence.  In  the  common  reports 
of  homophonic  harmony,  the  enumeration  of  which 
we  have  begun  and  will  continue,  we  have  found 
the  long-sought  key  to  common  music-feeling  and 
a  common  basis  for  testing  truth.  These  reports 
have  guided  us  in  explaining  and  verifying  the 
genesis  of  consonance  and  dissonance  in  one  voice, 
and  will  as  securely  guide  us  in  tracing  the  genesis  of 


ACCENT  AND  REGNANT  HARMONY  103 

new  homophonic  harmonies.  We  have  accounted  for 
the  genesis  of  the  foundation-group  of  seven  com- 
ponent tones  and  five  harmonic  percepts  of  the  origi- 
nal consonance  and  dissonance,  and  I  have  named 
this  original  group  the  Major  Tonic  and  its  cadences. 
From  this  original  group  new  forms  of  harmony  intro- 
ducing new  tones  and  new  harmonic  percepts  have 
been  derived.  How.?  Through  rhythmic  relation 
like  their  antecedents.  The  cause  of  the  genesis  of 
consonance  and  dissonance  we  discovered  to  be  the 
rhythm-derived  relation  of  cadence  and  repose. 
Rhythmic  relation  has  produced  all  subsequent 
new  forms  of  harmony.  The  psychology  of  this 
evolutionary  process  is  next  defined  in  terms  apply- 
ing to  every  stage  in  the  development  of  homo- 
phony.  Existing  tones  in  existing  relations  generate 
and  report  only  existing  forms  of  harmony,  while  in 
new  or  changed  relations  they  generate  and  report 
new  forms  of  harmony.  Next  we  will  apply  these 
principles  to  the  foundation-group  of  tones.  The 
seven  original  tones  in  their  original  relations  in 
cadence  and  repose  generate  and  report  only  the  origi- 
nal forms  of  harmony  in  which  they  arose,  while  in 
new  or  changed  relations  they  generate  and  report 
new  forms  of  harmony  introducing  new  tones  and 
new  harmonic  percepts.  The  evolution  of  harmony 
is  therefore  the  direct  cause  of  the  expansion  of 
tonality  and  consequent  expansion  of  the  tone-sys- 
tem. Each  developmental  step  in  music  was  there- 
fore dependent  on  and  due  to  the  evolution  of  har- 
mony, and  the  three  successive  and  interdependent 
stages  of  music,  namely,  homophony,  polyphony  and 


104  THE  NATURE  OF  MUSIC 

chords,  are  so  many  stages  of  harmonic  evolution. 
Hence  this  logical  conclusion.  Root,  trunk  and  over- 
spreading boughs,  all  music  from  first  to  last  is  one 
growth  of  one  psychological  tree  of  tone-relations  and 
forms  of  harmony.  All  tone-relations  and  forms  of 
harmony  in  one  voice,  where  did  their  genesis  take 
place.?  In  feeling,  under  the  impulse  of  indwelling 
causes.  In  what  form  were  they  first  embodied  and 
expressed  ?  In  melody,  the  original  voice  and  vehicle 
of  tone-language,  the  indissoluble  composite  of  rela- 
tion and  form  in  time  (rhythm)  and  relation  and 
form  in  space  (harmony),  the  essence,  heart  and  soul 
of  music.  All  that  is  essential  and  potential  in 
homophony  is  embodied  in  melody.  Thus  our  study 
of  homophony  resolves  itself  into  that  of  the  common 
reports  of  our  common  feeling  and  perception  of 
melody.  Are  we  not  all  of  us  melodists  ?  What  is 
all  primitive  music  but  primitive  melody,  formal 
music  but  conventional  melody,  modern  music  but 
free  melody.?  All  along  the  line,  are  not  all  the 
great  composers  melodists  ?  Are  not  their  works 
immortal  because  their  melodies  are  immortal.? 

This  introduction  to  the  several  chapters  before  us 
may  be  concluded  with  a  few  observations  which 
will  focus  our  attention  upon  the  special  subject 
directly  before  us.  One  regnant  harmony  after  an- 
other had  its  genesis  in  feeling  and  was  embodied 
in  and  reported  by  melody.  In  a  book  published 
fourteen  years  ago  ["  The  Septonate  "]  what  I  now  call 
harmony  in  one  voice  I  there  named  meloharmony, 
the  inherent  harmony  of  melody;  what  I  now  call 
regnant  harmony  I  there  named  ruling  or  governing 


ACCENT  AND  REGNANT  HARMONY  105 

harmony;  what  I  now  call  the  efficient  accent  was 
there  named  the  rhythmo-harmonic  accent  or  point. 

1.  The  evolutionary  sequence  of  ho  mo  phonic  har- 
monies is  a  sequence  of  regnant  harmonies  which 
melody  brought  forth  one  by  one  beginning  with  the 
regnant  Major  Tonic,  the  nucleus  in  relation  to  which 
the  others  arose.  A  regnant  harmony  asserts  itself 
during  every  moment  in  melody.  The  regnant  har- 
mony of  the  moment  selects  and  asserts  itself,  it 
determines  the  exact  harmonic  relation  of  each  tone 
in  melody  and  we  all  hear  it  in  common.  Therefore 
all  melodies  are  based  on  regnant  harmonies,  the 
simplest  on  one  such  harmony  (Major  Tonic),  the 
more  complex  on  two  or  more  such  harmonies. 

2.  The  efficient  accent  is  the  heavy  recurring 
rhythmic  accent  of  melody;  it  is  the  principle  of 
harmonic  genesis  and  development  in  homophony, 
and  has  generated  one  regnant  harmony  after  an- 
other. The  shortest  melody  consisting  of  two  tones 
has  but  one  efficient  accent:  the  cuckoo-song  is  an 
example.  Longer  melodies  are  connected  by  a  series 
of  such  accents.  As  a  melody  proceeds  from  one 
such  accent  to  another  one  of  two  things  happens: 
either  the  initial  regnant  harmony  is  maintained  and 
repeated,  or  a  new  regnant  harmony  is  generated.  We 
are  to  study  the  causes  in  both  cases.  Two  condi- 
tions were  indispensable  to  the  development  of  music 
beyond  the  stage  of  one  regnant  harmony,  the  Major 
Tonic.  These  were  first,  the  lengthening  of  melody 
from  one  efficient  accent  to  a  series  of  such  accents; 
second,  the  genesis  of  a  second  regnant  harmony. 

3.  The  component  tones  of  the  regnant  harmony 


106  THE  NATURE  OF  MUSIC 

are  named  regnant  tones.  The  tones  lying  over  and 
under  and  cadencing  up  and  down  into  the  regnant 
tones  are  named  bytones.  Bytones  are  components 
of  other  harmonies  named  byharmonies.  Regnant 
harmony,  regnant  tone;  byharmony,  by  tone;  let  us 
bear  these  terms  and  their  meanings  in  mind.  The 
first  regnant  tones  to  appear  in  melody  were  do,  mi, 
sol,  of  the  regnant  Major  Tonic :  the  first  bytones  to 
appear  were  the  original  cadence-tones  re,  la,  fa  and  ti, 
which  as  we  have  seen  arose  in  relation  to  the  Major 
Tonic-harmony.  Of  these  embryonic  melodies  there 
are  two  types:  first,  those  lowest  in  the  order  of 
development  composed  of  regnant  tones  only  and 
representing  harmonic  perception  and  harmonic  rela- 
tion in  their  incipiency  and  within  their  narrowest 
confines ;  second,  those  next  in  order  of  development, 
which  introduce  bytones  along  with  the  regnant  tones, 
thus  marking  an  advance  in  harmonic  perception 
and  relation.  Melody  based  on  one  regnant  harmony 
could  advance  no  further;  the  second  type  of  melody 
brings  its  first  chapter  of  development  to  a  conclusion, 
and  this  first  chapter  of  melody  corresponds  with 
the  first  developmental  chapter  of  harmony.  From 
first  to  last  the  development  of  melody  is  dependent 
on  that  of  harmony;  melody  could  not  advance 
another  step  until  a  second  regnant  harmony  arose 
in  relation  to  the  first.  When  this  step  was  taken 
a  significant  change  was  suddenly  effected,  for  at  one 
bound  harmonic  relation  expanded  from  that  of 
bytone  to  one  regnant  harmony  to  that  of  one  reg- 
nant harmony  to  another  regnant  harmony;  at  one 
bound  melody  entered  into  a  new  region  of  inexhaust- 


ACCENT  AND  REGNANT  HARMONY 


107 


ible  fertility  and  initiated  a  new  chapter  in  music- 
evolution,  the  end  of  which  has  not  yet  been  reached. 
Let  us  be  explicit  on  this  point.  Melody  started  with 
one  regnant  harmony  as  a  nucleus,  in  relation  to 
which  it  produced  other  regnant  harmonies,  in  relation 
to  which  it  produced  still  others,  and  so  on  ad  infini- 
tum, thus  evolving  an  ever  increasing  psychological 
web  of  correlated  threads  of  harmony.  How  then  did 
melody  recombine  the  seven  original  tones  in  new 
relations  which  generated  one  regnant  harmony  after 
another  ? 

4.  In  every  conceivable  combination  of  the  tones 
do,  mi,  sol,  melody  reports  the  regnancy  of  the  Major 
Tonic  (I).  In  other  words,  a  second  regnant  har- 
mony is  not  latent  or  potential  in  this  type  of  melody. 

5    1  3  5  3  1  5 


5.  Melody  first  introduced  bytones  on  its  light 
rhythmic  accents.  In  this  their  original  relation  the 
cadence-tones  re,  la,  fa  and  ti  do  not  disturb  the 
regnancy  of  the  Major  Tonic  and  could  not  have 
generated  a  second  regnant  harmony.  The  exam- 
ple below  presents  re  and  la,  which  are  the  first  two 
bytones  to  appear  in  melody,  re  in  cadence  to  do  and 
mediating  between  do  and  mi,  la  in  cadence  to  sol, 
1153351      35535 


i 


-•/-^ 


jW=rm. 


I 


108  THE  NATURE  OF  MUSIC 

6.  But  at  the  moment  when  melody  introduced 
re  and  la  on  its  heavy  rhythmic  accents  (eflBcient 
accents)  the  great  transformation  takes  place.  Sud- 
denly re  and  la  are  transformed  into  regnant  tones 
reporting  regnant  harmonies.  The  efficient  accent 
on  re  generates  the  regnant  Dominant-harmony  (V): 
the  efficient  accent  on  la  generates  the  regnant  Sub- 
dominant-harmony  (IV).  These  common  harmonic 
reports  of  melody  are  next  exemplified. 

51         5         353         535  1 

±=4 


i 


Pipy,  i  0  J  lF^J#^^=^^ 


IV 

Each  of  the  above  efficient  accents  reports  a  change 
of  regnant  harmony;  the  mode  relation  of  one  regnant 
harmony  to  another  is  at  once  established  in  this 
pentatonic  or  five-tone  stage  of  melody,  and  melody 
is  enriched  by  the  addition  of  two  new  regnant  har- 
monies. The  regnant  Major  Tonic,  as  we  have  seen, 
arose  independently  on  an  isolated  tone.  Not  so  with 
the  regnant  V  and  IV,  which  arose  in  relation  to  and 
were  dependent  on  the  previously  existing  regnant  I. 
This  dependence  on  and  genesis  in  relation  to  ante- 
cedent harmonies  distinguishes  all  other  harmonies 
from  the  original  regnant  I,  which  has  no  antece- 
dents. We  observe  further  that  while  the  regnant  I 
entered  into  being  by  way  of  do  its  root,  the  regnant 
V  was  first  represented  and  reported  by  re  its  ffth, 
the  regnant  IV  by  la  its  third.  Such  are  the  common 
reports  of  common  feeling  and  perception,  at  once 
the  simplest  and  surest  test  of  truth.     The  efficient 


ACCENT  AND  REGNANT  HARMONY  109 

accent  of  melody  has  generated  these  first  three 
regnant  harmonies  in  the  order  I,  V,  IV,  and  the  reg- 
nant harmony  of  melody  arises  of  itself,  asserts  itself 
and  is  unalterable  in  one  voice.  We  note  that 
evolving  melody  in  spinning  the  psychological  web 
of  correlated  threads  of  harmony  began  with  one 
thread,  do,  mi,  sol  of  I ;  melody  next  added  the  by  tones 
re  and  la  on  light  rhythmic  accents,  re  reporting  V  as 
byharmony,  la  reporting  IV  as  byharmony;  melody 
next  introduced  re  and  la  on  eflScient  accents  and  so 
produced  the  regnant  V  and  IV.  Thus  far  we  have 
traced  the  genesis  of  harmony,  and  the  addition  of 
the  regnant  V  and  IV  to  I  opens  new  channels  of 
development  and  so  many  changes  and  possibilities 
in  harmonic  relation  that  it  may  be  well  to  present 
the  more  noticeable  points  one  by  one. 

7.  The  melodies  in  our  last  two  examples  are 
pentatonic,  that  is,  composed  of  the  five  tones  do, 
re,  mi,  sol,  la,  which  we  have  abeady  identified  as 
the  pentatonic  scale.  Enough  has  been  explained 
to  show  the  archaeologist  that  in  his  endeavor  to 
establish  the  true  chronological  order  of  primitive 
melodies  his  conclusions  are  to  be  deduced  not  alone 
from  the  number  of  individual  tones  or  the  scale  of 
a  given  melody,  but  from  the  inherent  harmonic  con- 
tent and  relations  of  that  melody.  The  scale  is  not 
the  thing  of  essential  importance,  but  the  inherent 
harmony  is  the  important  thing,  the  true  guide  and 
test.  Melodies  composed  of  the  components  of  reg- 
nant I  exclusively  are  earliest;  melodies  containing 
the  bytone  re  are  later,  those  containing  the  bytone  la 
are  still  later;  those  containing  the  regnant  V  and  IV 


110  THE  NATURE  OF  MUSIC 

are  still  later.  The  pentatonic  stage  of  melody  is  evi- 
denced in  all  primitive  music  in  one  of  three  ways : 
either  these  melodies  precede  or  are  approaching  the 
pentatonic  stage,  or  they  have  reached  it  or  they  have 
passed  it.  Not  only  was  the  pentatonic  stage  the 
natural  product  of  the  progressive  development  of 
music  j>er  se,  but  the  entire  development  of  the  lan- 
guage and  art  of  music  up  to  the  present  time  was 
dependent  on  the  attainment  and  passage  remote 
ages  ago  of  the  pentatonic  stage  of  melody. 

8.  Certain  tones  like  do,  mi,  sol  and  others  first 
appeared  in  melody  in  the  relation  of  regnant  tones 
(components  of  regnant  harmonies).  Certain  tones 
like  re,  la  and  others  first  appeared  in  the  relation 
of  by  tones  (components  of  byharmonies).  We  have 
seen  how  V  and  IV  were  transmuted  from  byhar- 
monies to  regnant  harmonies.  We  are  about  to  see 
how  regnant  I  is  transmuted  into  a  byharmony. 
The  point  to  be  noted  here  is  this.  Every  such 
change  of  a  tone's  original  relation  to  a  new  relation 
marks  not  alone  the  progress  of  melody  consequent 
on  the  progressive  development  of  its  inherent  poten- 
tial harmony  and  harmonic  relations,  but  it  at  once 
marks  the  progressive  development  of  the  harmonic 
sense,  which  is  the  proximate  cause  of  the  progress 
of  melody  and  expansion  of  harmony,  and  which 
steadily  though  slowly  led  to  the  eventual  discovery 
or  perception  of  harmony  itself.  The  evolution  of 
harmonic  perception  affords  a  striking  example  of 
the  extreme  slowness  of  the  evolutionary  processes  of 
perception  in  general.  Although  from  the  first  and 
through  countless  ages  melody  has  asserted  its  inherent 


ACCENT  AND  REGNANT  HARMONY  111 

harmony,  yet  man's  discovery  or  perception  of  harmony 
and  its  introduction  in  the  form  of  chord  date  back 
but  a  few  centuries.  However,  this  great  slowness  is 
offset  by  what  followed,  for  this  discovery  of  harmony 
was  magical  in  its  effects,  initiating  as  it  did  an  era 
of  development  in  music  which  for  rapidity  of  pro- 
gress and  wealth  of  productivity  has  no  parallel  in 
psychology  and  history. 

9.  When  we  were  dealing  with  but  one  regnant  har-  ^^ 
mony  and  its  bytones  (Major  Tonic  and  its  cadences) 
the  term  repose  applied  exclusively  to  the  original  re- 
pose-harmony or  major  consonance  and  to  the  stable 
period  of  rhythm-repose  in  which  this  stable  harmony 
arose.  Then,  too,  the  term  cadence  applied  exclusively 
to  the  original  cadence-harmony  or  dissonance  and  to 
the  unstable  and  relative  period  of  rhythm-cadence  in 
which  this  unstable  and  relative  harmony  arose.  But 
now  that  we  have  introduced  three  regnant  harmonies 
all  this  is  changed.  Now  and  henceforth  the  terms 
cadence  and  repose  become  general  and  apply  to  rhyth- 
mic and  harmonic  forms  and  relations  in  general  while 
the  terms  hytone  and  byharmony,  regnant  tone  and 
regnant  harmony  become  the  specific  and  unmodifi- 
able  terms  of  analysis.  Thus,  for  example,  what  we 
hitherto  called  the  Major  Tonic  and  its  cadences  we 
now  specify  as  reg.  I  and  its  bytones.  Presently  we  are 
to  analyze  reg.  V  and  its  bytones,  reg.  IV  and  its  by- 
tones.  Here  let  us  note  the  fact  that  every  regnant 
harmony  has  its  relative  byharmonies. 

In  taking  up  the  analysis  of  the  broad  relation  of 
regnant  harmony  to  regnant  harmony  let  us  bear  in 
mind  the  following   general    truths:  1.    Every  tone 


112  THE  NATURE  OF  MUSIC 

reports  a  harmonic  form  and  relation.  2.  Every 
tone  reports  a  consonance  or  a  dissonance,  is  in 
cadence  or  repose,  is  a  by  tone  or  a  regnant  tone. 
3.  Every  step  from  tone  to  tone,  from  harmony  to 
harmony,  is  a  progression  or  a  resolution.  4.  All 
these  reports  are  common  reports. 

10.  The  regnant  harmony  of  the  moment  is  the 
repose  and  equilibrium  of  that  moment.  Whether  the 
regnant  harmony  of  the  moment  be  I  or  V  or  IV  or 
any  other  it  is  the  repose  and  equilibrium  of  that 
moment.  This  is  illustrated  in  our  last  example 
where  the  regnant  harmonies  appear  in  this  order, 
I — V — I — IV — I — V — ^I.  Here  we  note  the  wider 
application  of  the  term  repose  in  the  sense  of  the 
equilibrium  of  the  moment. 

1 1 .  The  regnant  harmony  of  one  moment  relates  to 
the  regnant  harmony  of  the  next  moment.  But  the 
relation  of  a  byharmony  is  confined  to  the  single 
moment  of  one  regnant  harmony.  See  last  example 
but  one.  The  basic  rhythmic  links  of  a  melody  are 
its  series  of  efficient  accents,  and  the  basic  harmonic 
links  of  a  melody  are  its  series  of  regnant  harmonies. 
Since  the  tones  that  fall  on  efficient  accents  generate 
and  report  the  regnant  harmonies,  and  since  the 
moment  from  one  such  accent  to  another  is  that  of 
one  regnant  harmony  to  another,  it  is  clear  that  these 
rhythmic  and  harmonic  links  of  melody  are  insepara- 
bly united  and  interdependent.  The  minute  analysis 
of  this  relation  of  and  movement  from  one  regnant 
harmony  to  another  now  confronts  us. 

12.  The  steps  from  I  to  V  and  I  to  IV  are 
progressions;   see   below  at   a)  and   c).     The   steps 


ACCENT  AND  REGNANT  HARMONY 


113 


from  V  to  I  and  IV  to  I  are  resolutions ;  see  below  at 
b)  and  d).  In  these  resolutions  V  and  IV  are  in 
cadence  to  I.  Here  note  the  wider  application  of  the 
term  cadence  in  this  connection  with  regnant  harmony. 
Though  the  regnant  harmony  of  the  moment  is  the 
repose  and  equilibrium  of  the  moment,  we  observe 
at  b)  and  d)  that  it  may  be  in  cadence,  that  is,  in 
unstable  equilibrium. 
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In  the  progression  I — ^V  at  a)  re  reports  V  as 
consonance  with  sol  as  concomitant  1  and  ti  as  con- 
comitant 3.  But  in  the  resolution  and  cadence  V — I 
at  b)  re  reports  V  as  dissonance,  and  in  this  cadence- 
relation  all  the  original  cadence- tones,  namely,  ti,  rCy 
fa  and  la,  assert  themselves  as  components  of  the 
genus  dissonance  in  that  they  each  and  all  claim  sol 
as  their  common  root.  Not  until  melody  had  pro- 
duced regnant  V  in  this  cadence-relation  was  it  pos- 
sible for  la  to  assert  itself  as  9.  This  genesis  of 
regnant  V  in  cadence  belongs  to  melody's  pentatonic 
stage  and  was  generated  by  the  efficient  accent  on  re. 
During  this  stage  sol  which  already  existed  as  5  of 
I  could  next  be  related  as  1  of  V,  and  la,  which  already 
existed  as  a  bytone  and  as  3  of  the  byharmony  IV, 
could  next  be  related  as  9  of  V.  In  short,  during 
this  stage  melody  became  enriched  by  many  new 
intervals  resulting  from  the  combinations  of  re,  sol 
and  la  during  the  regnancy  of  V  in  cadence.  Illus- 
trations of  some  of  these  intervals  follow. 


114  THE  NATURE  OF  MUSIC 

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7  of  V  were  differentiated  as  individual  tones  the 
melody  emerged  from  its  pentatonic  stage  and  was 
again  enriched  by  many  new  intervals  resulting  from 
combinations  of  sol^  re  and  la  with  ti  and /a  during 
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ACCENT  AND  REGNANT  HARMONY 


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Here  note  the  fact  that  regnant  V  is  sometimes  a 
consonance,  sometimes  a  dissonance  with  four  com- 
ponents as  V?,  sometimes  a  dissonance  with  five 
components  as  V9.  Hence  this  general  truth:  The 
regnant  harmony  of  the  moTnent  may  be  either  a  con- 
sonance or  a  dissonance. 

Attention  is  again  called  to  the  first  example  of  this 
paragraph.  Both  in  the  progression  I — ^IV  at  c)  and 
the  resolution  IV — I  at  d)  regnant  IV  is  reported 
a  consonance  by  la.  In  both  relations  la  reports  do 
as  concomitant  5  and /a  as  concomitant  1.  Regnant 
IV  again  enriches  melody  with  new  intervals  result- 
ing from  combinations  of  its  components/a,  la  and  do. 
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116  THE  NATURE  OF  MUSIC 

Here  we  observe  that  regnant  IV,  though  it  is 
a  consonance,  is  in  cadence  to  I.  Hence  this  truth : 
Consonances  as  well  as  dissonances  may  be  in  cadence. 
Further  analysis  will  extricate  us  from  what  here 
threatens  to  become  a  tangle  of  terms.  This  may  be 
avoided  by  at  once  stating  the  following  general  truth 
which  opens  up  and  covers  the  whole  subject  of 
regnant  harmony  and  its  byharmony.  Both  byhar- 
monies  and  regnant  harmonies  may  be  either  conso^ 
nances  or  dissonances :  the  former  are  always  in  cadence 
or  unstable  equilibrium,  the  latter  may  be  either  in 
repose  (stable  equilibrium)  or  in  cadence  (unstable 
equilibrium).  Byharmony  and  dissonance,  regnant 
harmony  and  consonance,  these  are  not  interchange- 
able terms.  Confusion  of  these  terms  will  result  in 
complete  confusion.  Distinction  between  these  terms 
will  preserve  complete  clarity. 

13.  In  the  harmonic  analysis  of  melody  the  series 
of  questions  to  be  answered  are  these:  1.  What  is 
the  regnant  harmony  of  the  moment  ?  Is  its  form  a 
consonance  or  a  dissonance  ?  What  are  the  regnant 
tones  and  their  relations  ?  2.  What  are  the  bytones, 
their  relations,  the  forms  of  harmony  they  represent  ? 
These  leading  analytical  questions  apply  to  all  music 
since  music  the  world  over,  past  and  present,  primitive 
and  modern,  one-voice  and  multi-voice,  is  one  in  kind. 
These  questions  therefore  apply  to  bird-melodies  as 
well  as  human  melodies,  to  oriental  as  well  as  occi- 
dental music,  to  Greek  and  Ecclesiastical  melodies 
as  well  as  to  folksongs  and  dances,  sonatas  and 
symphonies. 

14.  Owing    to    the    changes    from    one  regnant 


ACCENT  AND  REGNANT  HARMONY 


117 


harmony  to  another  reported  by  the  efficient  accent 
of  melody  each  of  the  seven  diatonics  appears  now 
as  a  regnant  tone,  now  as  a  bytone.  Thus  what  is 
a  regnant  harmony  at  one  moment  is  transmuted 
into  a  byharmony  the  next  moment  and  the  reverse. 
Our  next  example  presents  I  with  bytones,  V  with 
bytones  and  IV  with  bytones,  and  all  these  regnant 
harmonies  and  byharmonies  are  diatonic.  A  har- 
mony is  classed  as  diatonic  when  all  its  concomitants 
or  components  are  diatonic. 

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Except  at  N.B.  all  the  above  regnant  harmonies 
are  consonances.  Except  at  N.B.  the  second  tone  in 
each  measure  is  a  bytone,  but  this  second  tone  in 
every  measure  including  N.B.  is  in  cadence.  With 
one  exception  all  the  byharmonies  are  consonances 
in  cadence.  The  exception  is  reported  by /a  during 
the  regnancy  of  I  when  the  byharmony  is  a  four- 
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118  THE  NATURE  OF  MUSIC 

N.B.  the  regnant  harmony  is  V9  owing  to  the  presence 
of  la  which  is  at  once  a  regnant  tone  and  in  cadence 
and,  strange  to  say,  resolves  into  its  own  harmony. 
The  ninth  is  the  first  harmonic  component  distin- 
guished by  these  pecuHarities,  especially  that  of 
resolving  into  its  own  harmony,  and  la  being  the 
original  ninth  it  was  the  first  tone  that  appeared  in 
this  paradoxical  relation.  This  characteristic  insta- 
bility of  la  as  ninth  during  the  regnancy  of  V,  caused 
by  its  position  beyond  the  octave  of  its  root,  will  be 
further  illustrated  as  we  proceed  seriatim  to  analyze 
the  diatonic  bytones  of  each  of  the  three  regnant 
harmonies  under  consideration.  Let  us  remember 
that  at  present  we  are  dealing  exclusively  with  dia- 
tonic harmonies  as  defined  a  moment  ago. 

A,  The  diatonic  bytones  of  reg.  I  are  ti  3,  re  5, 
fa  7,  la  3.  During  this  regnancy  these  bytones  persist 
each  in  the  harmonic  report  just  given.  Even  when 
playing  upon  the  same  regnant  tone  fa  and  la  persist 
in  their  respective  reports  as  r  and  3  as  will  be  heard 
in  the  following  fugue-subject  of  Bach  here  tran- 
scribed from  Cj^  to  C  Major:  — 

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Previous  examples  present  a  sufficient  number  of 
illustrations  of  these  bytones,  and  what  still  remains  to 
be  said  of  them  will  be  found  in  the  chapter  on  cadences. 

B,  During  the  regnancy  of  V  there  are  but  two 
diatonic  bytones,  namely,  do  1  and  mi  3  as  follows :  — 


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The  bytone  do  plays  on  regnant  ti  and  re,  the 
by  tone  mi  plays  on  regnant  re  and /a.  The  cadences 
of  regnant  la  to  regnant  sol  and  <i  appear  in  the 
first  two  measures  and  are  emphasized  through 
jermaias  in  the  last  two  measures.  These  steps  of 
do,  mi  and  la  are  the  only  cadences  in  our  example, 
all  the  other  steps  being  progressions  from  one  reg- 
nant tone  to  another. 

C.  Regnant  IV  has  four  diatonic  bytones.  They 
are  mi  3,  sol  5,  ti  3,  re  5.  Unless  we  generate  the 
feeling  of  regnant  IV  we  cannot  perceive  the  true 
harmonic  relations  and  reports  of  its  bytones.  In  the 
subjoined  example  of  the  common  reports  of  these 
bytones  the  feeling  of  IV  is  generated  in  the  opening 
measures. 


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120  THE  NATURE  OF  MUSIC 

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Noteworthy  among  these  reports  are  the  series  of 
major  thirds  3 — 3 — 3  (third  last  measure)  and  the 
series  of  pure  fifths  5 — 5 — 5  (second  last  measure). 
These  reports  have  a  bearing  on  certain  important 
harmonic  questions  to  be  considered  later  on.  We 
have  now  presented  the  diatonic  bytones  of  each  of 
the  harmonies  I,  V  and  IV. 

15.  Certain  changes  in  the  rhythmic  distribution 
of  regnant  tones  and  bytones  mark  concomitant 
changes  from  an  earlier  to  a  later  stage  of  melohar- 
monic  development,  therefore  of  psychological  devel- 
opment. Most  of  the  examples  thus  far  given  illus- 
trate the  earlier  of  the  two  stages  when  regnant 
tones  and  bytones  occupied  the  rhythmic  periods  in 
which  they  first  arose,  the  former  appearing  on  the 
heavy  (efficient)  periods  of  rhythm-repose,  the  latter 
on  the  light  and  unstable  periods  of  rhythm-cadence. 
Rhythmic  movements  being  characterized  by  regular 
alternations  of  light  and  heavy  periods  and  accents, 
that  is,  by  regular  alternations  of  rhythm-cadence 
and  rhythm-repose  in  obedience  to  the  universal 
shaping  principle  of  equilibrium,  we  may  define  this 
basic  and  universal  relation  of  rhythmic  cadence  and 
repose  as  that  of  a  rhythmic  Dominant  to  a  rhythmic 
Tonic,  since  the  intoning  of  this  relation  caused  the 
genesis  of  dissonance  (V9)  in  rhythm-cadence  and 
consonance  (I)  in  rhythm-repose,  therefore  of  the  real 


ACCENT  AND  REGNANT  HARMONY 


121 


Dominant  and  the  real  Tonic.  The  distribution  of 
regnant  tones  and  bytones  illustrative  of  melodies  be- 
longing to  the  earlier  of  the  two  stages  is  as  follows :  — 

Coincident  rhythm-repose  (heavy period  and  accent) 
and  tone-repose  (regnant  tone). 

Coincident  rhythm-cadence  (light  period  and  ac- 
cent) and  tone-cadence  (by tone). 

The  later  of  the  two  stages  is  illustrated  by  melodies 
in  which  regnant  tones  and  bytones  exchange  their 
original  rhythmic  positions,  the  former  occupying 
the  cadence-periods,  the  latter  occupying  the  repose- 
periods  of  rhythm,  as  follows:  — 

Coincident  rhythm-repose  (heavy  period  and  accent) 
and  tone-cadence  (by tone). 

Coincident  rhythm-cadence  (light  period  and  ac- 
cent) and  tone-repose  (regnant  tone). 

This  shifting  of  bytones  from  light  to  heavy  rhythmic 
periods  indicates  a  great  advance  in  the  development 
of  melody  consequent  on  that  of  the  harmonic  sense. 
Illustrations  appear  below. 

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THE  NATURE  OF  MUSIC 


Further  illustrations  of  diatonic  bytones  will  appear 
in  the  chapter  on  cadences. 

16.  The  truth  that  a  tone's  specific  harmonic 
form  is  caused  by  its  specific  combined  relation  in 
time  and  space  has  been  and  will  continue  to  be 
demonstrated.  Thus  far  each  of  the  seven  diatonics 
(original  tones)  ifas  appeared  as  a  regnant  tone  and 
as  a  bytone,  and  has  reported  one  of  the  five  original 
harmonic  percepts  1  or  3  or  5  or  7  or  9.  Thus  far 
each  of  the  seven  has  appeared  in  the  following 
harmonic  relations:  do  as  1  of  I  and  as  5  of  IV;  mi 
as  3  of  I;  sol  as  5  of  I  and  as  1  of  V;  ti  as  3  of  V; 
re  as  5  of  V;  fa  as  7  of  V  and  1  of  IV;  la  as  9  of  V  and 
3  of  IV.  This  summary  shows  that  four  diatonics 
(do,  sol,  fa  and  la)  have  appeared  each  in  two  har- 
monies, while  the  remaining  three  (mi,  re,  ti)  have 
appeared  only  in  one  harmony.  The  former  are 
bond-tones  or  connecting  links  between  two  har- 
monies. Of  these  sol  is  the  first  and  the  nexus 
between  I  and  V,  I  and  V,,  I  and  V9  as  follows:  — 
1       3      5^^^  13      5^9 

I  Do  —  mi  —  5oZ  I V 

I         V, 

V9 

The  next  bond-tone  is  do,  the  nexus  between  I 

and  IV. 

1      3      5^.-^l       3      5 

Fa  —  la  —  do  Do  —  mi  —  sol 


Sol  —  ti  —  re  \—fa 

—  la 

IV  I 

Sol,  being  the  original  bond-tone  and  first  connect- 
ing link  between  two  harmonies,  was  the  first  of  the 


ACCENT  AND  REGNANT  HARMONY  123 

seven  diatonics  to  undergo  a  change  of  relation, 
namely,  from  5  to  1.  Next  to  follow  was  do,  chang- 
ing its  relation  from  1  to  5.  These  bond-tones  plainly 
indicate  that  the  roots  of  the  two  harmonies  which 
each  connects  lie  sl  fifth  apart.  Thus  I — V  connected 
by  sol  and  I — IV  connected  by  do  are  called  fifth- 
related  harmonies.  These  fifth-related  harmonies  are 
not  only  the  first  of  their  kind,  but  are  the  first  of  any 
kind.  This  explains  why  fifth-related  harmonies  are 
nearest  related  harmonies,  why  fifth-related  keys  are 
nearest  related  keys.  These  fifth-relations  also  dis- 
close the  origin  of  the  authentic  closing-cadence  V — I, 
of  the  plagal  closing-cadence  IV — I  and  of  the  fifth- 
cycle  of  keys.  In  these  diatonic-Major  relations  the 
bond-tones  sol  and  do  are  in  repose  and  stable,  and 
this  is  true  of  all  bond-tones  of  fifth-related  harmonies. 
The  case  is  otherwise  with  the  bond-tones  fa  and  la 
which  in  all  the  relations  thus  far  presented  main- 
tain their  unstable  character,  which  is  explained  by 
the  fact  that  they  belong  to  the  genus  dissonance. 
Whether  as  bytones  to  I  or  as  regnant  tones  in  V9 
and  IV  or  as  bond-tones  connecting  V9 — ^IV  and 
IV — ^V9,  both  fa  and  la  manifest  this  unstable  char- 
acter, and  they  do  not  gain  repose  and  stability  until 
they  appear  in  Minor  as  we  shall  see  in  the  next 
chapter.  Meanwhile  I  present  them  as  connecting 
links  between  V9  and  IV. 


124  THE  NATURE  OF  MUSIC 

17.  As  defined  on  a  previous  page,  a  harmony 
is  diatonic  when  all  its  components  are  diatonics. 
The  test  of  the  pure  diatonic  harmonies  of  melody, 
in  fact  of  all  the  harmonic  forms  and  relations  of 
melody,  lies  in  the  common  reports  of  original  har- 
mony in  one  voice.  In  one  voice  a  diatonic  in  certain 
relations  generates  a  thread  of  harmony  in  which  all 
the  concomitants  are  diatonics,  while  in  certain 
other  relations  the  same  diatonic  generates  a  thread 
of  harmony  among  whose  components  there  are 
chromatics  and  even  enharmonics  mingling  with 
diatonics,  as  we  shall  see  in  the  sequel.  Here  we  are 
concerned  with  pure  diatonic  harmonies.  I,  V,  V^, 
V9  and  IV  are  diatonic  harmonies  and  the  only  ones 
in  the  Major  mode.  All  forms  of  harmony  are  con- 
sonances or  dissonances.  Each  specific  form  of  conso- 
nance and  dissonance  had  its  genesis  on  a  specific 
tone  in  a  specific  relation,  and  each  such  original  form 
is  a  prototype.  Once  generated  and  differentiated 
each  prototype  is  reproduced  and  repeated  on  other 
tones  also  in  specific  relations.  The  harmonies  thus 
far  generated  will  serve  as  an  illustration.  I,  V  and 
IV  are  major  consonances :  I  is  the  prototype  of  this 
specific  form  and  it  first  arose  on  do  1;  V  and  IV  are 
reproductions  and  replicates,  the  former  arose  on  re  5, 
the  latter  on  la  3.  Again,  V^  and  V9  are  major  dis- 
sonances, and  both  are  prototypes  of  their  respective 
forms  of  which  all  like  forms  are  replicates.  This 
concludes  the  summary  of  the  diatonic  harmonies  of 
the  Major  mode.  In  the  next  chapter,  the  subject  of 
which  is  the  origin  of  the  Minor  harmony  and  mode, 
we  shall  encounter  three  other  diatonic  harmonies  and 


ACCENT  AND  REGNANT  HARMONY  125 

new  forms  of  consonance  and  dissonance,  all  of  which 
are  minor, 

18.  The  operation  of  the  principle  of  harmonic 
genesis  and  regnant  harmony,  the  efficient  accent, 
has  now  been  exemplified.  We  shall  resume  these 
subjects  later  on,  but  before  dismissing  them  here 
it  may  be  well  to  pause  and  observe  the  operation 
of  this  principle  with  greater  scrutiny.  We  have 
noted  that  alternating  rhythm-periods  make  for 
rhythmic  equilibrium,  that  alternating  tone-rhythmic 
periods  make  for  combined  rhythmo  -  harmonic 
equilibrium,  in  short,  that  the  connection  between 
harmonic  equilibrium  and  rhythmic  equilibrium  is 
indissoluble,  and  that  rhythm  has  transmuted  chaos  of 
sound  into  perfect  tone-equilibrium  or  harmony.  The 
shortest  rhythm  contains  two  periods.  The  shortest 
melody  contains  two  tones  each  occupying  a  rhythm 
period,  one  light,  one  heavy.  Thus  the  combined 
form  and  equilibrium  of  composite  rhythm  and 
harmony  is  conditioned  by  recurrence  of  these  alter- 
nating light  and  heavy  periods.  Let  the  following 
wave-lines  indicate  these  alternating  periods,  first, 
in  the  order  light-heavy;  next,  in  the  order  heavy- 
light,  and  let  the  repetition  marks  indicate  recurrence. 

1  .\  light  /  heavy^ :  1 1       2.    /  heavy\   light /:  1 1 

r       r  r      r 

The  notes  indicate  respectively  short-Zongr,  long- 
short;  the  dynamic  =^  indicates  the  efficient  accent. 
Now  sing  each  diatonic  whole  step  and  half  step  in 
accordance  with  these  two  forms  of  rhythm  and  note 


126 


THE  NATURE  OF  MUSIC 


the  operation  of  the  ejBSeient  accent  as  it  generates  and 
reports  the  regnant  harmony  and  determines  which 
of  the  two  tones  is  regnant  and  which  is  a  bytone. 
The  general  result  will  be  as  follows:  The  tone  that 
falls  on  the  light  and  short  accent  is  the  bytone  and 
component  of  the  byharmony,  while  the  tone  that 
falls  on  the  heavy  and  long  accent  (efficient  accent) 
is  the  regnant  tone  reporting  the  regnant  harmony 
of  which  it  is  a  component.  I  first  present  the 
ascending  steps. 

a)       15         15    6)  53         53    c)  31 


VI  IV  IV 


4) 


V 
5 


0  5 


m 


^^ 


5      3    /)  9     3 


IV 

3    g)3     I 


IV 
3      1 


^    J  UP    .|uJ=^:J|r    ■Irn-ti 


I  N.B.  V  IV 

Next  follow  the  descending  steps, 
a)  13  1         3      6)3      I 


i 


fir^I^dSL^t^m 


e) 


V  I 

3      5         3      5    d)5    1 


IV  V        N.B. 

O        7      e)  7      O 


m 


^ 


IV 


IV 


ACCENT  AND  REGNANT  HARMONY 


127 


1      3    /)  3     5 


a 


g) 


5     1 


^m 


5     1 


^ 


w 


i 


IV 


t 


At  N.B.  in  both  above  groups  of  examples  we 
again  encounter  la  9  playing  the  part  of  a  bytone 
during  the  regnancy  of  the  harmony  of  which  it  is 
a  component.  Attention  is  called  to  the  fact  that 
except  at  N.B.  the  form  of  all  the  above  regnant 
harmonies  is  that  of  a  consonance.  Here  we  observe 
the  general  truth  that  the  efficient  accent  everywhere 
makes  for  the  stable  equilibrium  of  consonance  except 
in  cases  like  N.B.  where  specific  relations  of  specific 
tones  cause  the  regnant  harmony  to  take  the  form 
of  a  dissonance.  The  above  examples  illustrate 
another  series  of  facts.  First,  we  observe  that  in 
certain  relations  a  regnant  consonance  is  generated 
by  the  efficient  accent  on  a  single  component  as  indi- 
cated by  the  tones  reporting  I,  V  and  IV;  second,  a 
regnant  dissonance  (see  N.B.)  is  not  generated  unless 
at  least  two  of  its  components  occupy  successive 
rhythm-periods.  We  will  first  take  up  the  conso- 
nances I,  V,  IV.  All  the  components  of  I  possess 
this  individual  power  to  generate  its  regnancy,  do 
by  itself,  mi  when  preceded  by  IV  or  V,  sol  when 
preceded  by  IV,  as  shown  below  at  a).  Two  com- 
ponents of  V  have  this  individual  power;  they  are  re 
and  ti;  see  below  at  b).  Two  components  of  IV 
have  this  individual  power,  namely,  la  and /a;  see 
below  at  c). 


128 

a) 


THE  NATURE  OF  MUSIC 
5      3      5        3      13       5 


i 


f 


6) 


IV_ 

3       5 


IV 

1      3 


J       V_ 

c)l     5 


i 


i 


I V       I 

5      11        8     11 


I IV 

5     13        5 


i 


I 


^ 


^ 


^ 


-gi — -» 


L 


IV 


IV      L 


IV 


In  its  diatonic  relations  sol  cannot  report  itself  as  1 
of  V  except  in  conjunction  with  another  component  of 
V.  The  same  is  true  of  do  as  5  of  IV.  This  explains 
why  in  their  diatonic  relations  sol  individually  cannot 
generate  regnant  V  and  do  individually  cannot  gen- 
erate regnant  IV. 

The  regnant  dissonances  V^  and  V9  next  claim 
our  attention.  Both  of  these  regnant  dissonances 
require  a  succession  of  at  least  two  components  to 
generate  them,  and  in  generating  regnant  V^  fa  must 
be  one  of  the  two,  while  in  generating  regnant  V9 
la  must  be  one  of  the  two.  Examples  of  both  are 
given  below,  regnant  V^  at  a),  regnant  V9  at  6). 


a) 


5       3 


i 


V. 


ACCENT  AND  REGNANT  HARMONY 


129 


^m 


*) 


I        V^ I         Vv I 

95535      95393       1 


i 


^ 


^ 


-#— 


g 


V9. 


I 


V9. 


V9. 


I 


3     9      5      1     ,5913     35     931 


i 


s 


I 


V9. 


V9. 


V9. 


Alternating  rhythmic  periods  are  the  elements  of 
rhythmic  form;  a  rhythmic  form  is  therefore  a 
succession  of  elements.  Harmonic  components  are 
the  elements  of  harmonic  form;  a  harmonic  form  is 
therefore  a  concurrence  of  elements.  Every  such  con- 
currence occupies  a  rhythm-period:  thus  when  we 
relate  one  such  concurrence  to  another  we  are  moving 
from  one  rhythmic  period  to  another,  and  this  con- 
currence (harmony,  form  and  relation  in  space)  and 
succession  (rhythm,  form  and  relation  in  time)  are 
indissolubly  combined.  It  is  therefore  perfectly  nat- 
ural that  regularly  alternating  rhythm-periods  of 
cadence  and  repose  should  have  caused  corresponding 
concomitant  alternations  of  regnant  harmonies  in 
cadence  and  repose,  since  both  in  rhythm  and  in  har- 
mony cadence  is  tend  and  repose  is  end  of  tend.  One 
illustration  will  suffice. 

3135151353531 


^ 


i 


IV 


^ 


I 


130 


THE  NATURE  OF  MUSIC 


Such  examples  of  concurrent  alternations  of  rhythmic 
and  harmonic  cadence  and  repose  manifest  the  direct 
influence  of  rhythm  upon  the  harmonic  structure  of 
melody,  while  on  the  other  hand  the  direct  influence 
of  harmony  upon  the  rhythmic  structure  of  melody 
is  manifested  in  the  lengthening  of  the  rhythmic 
periods  of  alternating  cadence  and  repose  from  beats 
to  measures.  These  reciprocal  influences  of  the  two 
elements,  now  of  rhythm  on  harmony,  now  of  harmony 
on  rhythm,  the  two  always  inseparably  combined  yet 
acting  and  reacting  each  upon  the  other  in  obedience 
to  the  inherent  shaping  principle  of  equilibrium,  these 
are  the  chief  shaping  forces  in  the  evolution  of  the 
musical  phrase  and  thence  of  the  larger  forms  of 
music.  I  will  pause  here  a  moment  to  point  out 
how  harmony  may  contract  and  expand  the  rhythmic 
form.  In  contractions  secondary  eflScient  accents 
appear  within  the  limits  of  one  measure  (see  below  at 
a))  while  in  expansions  the  regnant  harmonies  may 
extend  indefinitely  and  cause  the  rhythmic  forms  to 
be  either  perfectly  regular  (see  b))  or  irregular 
(see  c)). 


o) 


31351513 


^^ 


^ 


IV 


3135  1513 


etc.  or 


etc.  or 


$ 


3    1 


35151353573135 


IV 


— I 1— 

3^ 


i 


ACCENT  AND  REGNANT  HARMONY         131 
5)      3135  3  13  5 


^ 


etc.  or 


0) 


I  V 

8    13      5 


^ 


? 


etc. 


513 


3    5 


^ 


i 


:^=Sia! 


f^^4 


^ 


etc.  or 


V. 

5 


_IV 
5    3     5 


Fq^rap^ 


i 


I 


i 


IV 


The  next  examples  illustrate  the  prolongation  of 
harmonic  cadence  in  the  progressions  V — IV  and 
IV— V  at  a),  IV— V,  at  h). 


I 


\ 


.IV 


IV. 


« 


359315        35 


1     3 


i 


Hir   nN 


I 


P 


t 


V9 


IV. 


At  a)  as  we  move  from  <i  3  to  /a  3  and  vice  versa 
the  concomitant  harmonies  report  progressions  in 
parallel  fifths  and  octaves  which  though  unseen  are 
there  and  are  heard.     Such  parallels  are  unavoidable. 

A  general  survey  of  the  foregoing  analysis  of 
regnant  harmony  and  the  eflBcient  accent  enables  us 


132 


THE  NATURE  OF  MUSIC 


to  ask  and  answer  a  comprehensive  question.  Under 
what  conditions  does  the  change  from  one  regnant 
harmony  to  another  take  place  ?  This  change  takes 
place  when  a  hytone  of  the  momentary  harmony 
falls  on  the  efficient  accent.  The  following  examples 
present  these  bytone-changes  on  single  diatonics,  and 
a  few  chromatics  are  also  introduced  in  anticipation 
of  their  subsequent  explanation. 


i 


3     5     3 


5313       1353 


J=^=T^ 


lY      I 


3    15 

-Bh — I 0- 


II 


13     5     1 


'-t^ 


eS: 


\] 


-IV 


etc 


This  change  also  takes  place  when  certain  single 
bond-tones  fall  on  the  efficient  accent.  The  first  of 
these  bond-tone  changes  of  regnant  harmony  is 
reported  by  the  single  diatonic  sol  as  follows:  — 


5    9     15 


5      5^5915 


i 


m 


i=F- 


i 


-j|) ^^^5^ 


V9 


In  this  melody  from  Beethoven's  E  flat  concerto 
the  bond-tone  sol  instantaneously  changes  from  1  of 
V  to  5  of  I.  In  such  bond- tone  changes  of  regnant 
harmony  two  secondary  causes  cooperate  with  the 


ACCENT  AND  REGNANT  HARMONY         133 

efficient  accent,  first  the  tendency  to  resolve  disso- 
nance, next  the  regular  alternation  of  harmonic 
cadence  and  repose,  both  of  which  I  have  already 
explained. 

The  foregoing  analyses  demonstrate  that  original 
harmony  in  one  voice  reports  the  exact  number  of 
components  in  a  harmonic  thread;  three  components 
in  I,  V  and  IV,  four  in  V7,  five  in  V9.  They  demon- 
strate that  whenever  and  wherever  it  is  potential  in 
a  relation  the  efficient  accent  makes  for  a  regnant 
consonance,  that  is,  for  stable  equilibrium.  They 
demonstrate  that  the  form  of  regnant  harmony 
generated  by  the  efficient  accent,  be  it  consonance  or 
dissonance,  is  always  a  question  of  the  momentary 
relation  and  is  always  the  equilibrium  of  the  moment, 
consonance  being  stable,  dissonance  being  unstable 
or  relative  equilibrium. 

39.    Chords  Derived  from  the  Original  Consonance 
and  Dissonance  in  One  Voice 

From  the  prototype  consonance  I  are  derived  the 
diatonic-Major  triads  I,  V,  IV  known  as  the  three 
primary  chords. 


i 


s^i^ 


W=w^&^^^^ 


I         Y       IV  IV        I        V 

The  common  reports  of  original  harmony  in  one 
voice  for  the  first  time  demonstrate  and  prove  the 
truth  that  these  triads  may  be  represented  by  single 
components  as  well  as  by  any  two  or  by  all  three. 
Every  conceivable  combination  of  two  or  three  tones 


134 


THE  NATURE  OF  MUSIC 


lies  in  these  harmonic  threads  and  may  represent 
each  of  these  triads.  Of  the  many  possible  repre- 
sentations of  the  triad  I,  I  present  the  following:  — 


i 


-<2;t- 


i 


I 


I 


I 


4 


etc. 


m. 


t 


jO.- 


'J21 


-^- 


etc. 


The  triad  V  may  be  represented  by  the  single  com- 
ponents re  5  and  ti  3,  the  triad  IV  by  the  single 
components  la  3  and  fa  1.  Both  triads  V  and  IV 
may  appear  in  any  of  the  above  two-tone  and  three- 
tone  forms. 

From  the  prototype  dissonances  in  one  voice,  V9 
and  Vy,  are  derived  the  corresponding  chords  of  the 
ninth  and  seventh,  also  the  chord  vii^^.  Besides  these, 
the  dissonance  V9  breaks  up  into  three  triads.  All 
are  given  below  in  the  order  of  their  mention. 


m 


^- 


3         5 


e 


1.  Chord  Roots.    V9 

2.  Original  Root.  V9 


V9 


V 
V 


V9 


ACCENT  AND  REGNANT  HARMONY         135 

Like  the  harmonic  report  of  a  single  tone  so  also 
that  of  a  chord  is  determined  by  the  relation  in  which 
it  appears  and  varies  as  the  relation  varies.  All  the 
above  chords  in  their  diatonic-Major  relations  claim 
sol  as  their  common  harmonic  root.  Hence  the  above 
distinctions  and  discrepancies  between  chord-roots 
and  original  harmonic  roots.  Any  tone  may  be  taken 
as  a  chord-root.  Thus  a  chord-root  may  be  an 
original  harmonic  root  as  in  V9,  V^  and  V,  or  it  may 
be  a  harmonic  third  as  vii^y  and  vii°  or  a  harmonic 
fifth  as  II.  The  important  fact  to  be  observed  here 
is  that  certain  chord-forms  of  harmony  are  detached 
from  their  original  harmonic  roots.  To  regard  the 
roots  of  the  chords  vii^^,  vii°  and  ii  as  harmonic 
roots  and  to  symbolize  them  as  i  is  to  create  the 
greatest  possible  confusion  in  the  mind  owing  to  the 
irreconcilable  conflict  and  utter  discord  between  a 
thing  and  its  symbol,  between  what  we  really  hear 
and  feel  and  know  to  be  true  and  what  we  are  con- 
strained arbitrarily  to  think  and  what  we  know  to  be 
false.  Hence  this  truth:  No  given  chord  in  a  given 
relation  is  perfectly  comprehended  unless  we  subject 
it  to  the  common  reports  of  common  harmonic  feel- 
ing and  perception.  Hence  the  necessary  distinction 
between  harmonic  analysis  with  true  reports  and 
chord-analysis  with  false  reports.  We  shall  meet  all 
the  above  chords  in  transmuted  relations  when  we 
take  up  the  Minor  mode.  Here  attention  is  called 
to  the  important  chord  vii^^,  which  is  composed  of  the 
four  original  cadence-tones  and  which  I  name  the 
Major-cadence-seventh-chord.  In  resolution  its  two 
lower  tones  rise,  its  two  upper  tones  fall  as  below 


136  THE  NATURE  OF  MUSIC 

at  a).  Chords  whose  components  simultaneously  rise 
and  fall  have  double  cadences.  Chords  whose  cadences 
rise  only  or  fall  only  have  single  cadences.  Below  at 
b)  and  c)  the  double  cadence  of  vii%  is  separated 
into  single  cadences.  At  6)  sol  is  added  to  the  two 
lower  tones  of  vii^^,  thus  forming  the  triad  V 
and  becoming  the  bond-tone  of  the  original  rising 
chord-cadence  V — I,  the  authentic  ending.  At  c) 
do  is  added  to  the  two  upper  tones  of  vii^^,  thus 
forming  the  triad  IV  and  becoming  the  bond-tone 
of  the  original  falling  cadence  IV — I,  the  plagal 
ending. 


7 


5        5        1         5       5         3         5 
533533  13 

a)  3        1     ^)1        3         1    c)i  5        1 


vii^       I        V        V—    I      IV     lY—  I 

In  this  separation  of  the  original  cadence-tones  in 
the  triads  V  and  IV,  re  and  ti  retain  their  original 
relations  as  5  and  3  respectively  while  the  relations 
of  la  and  /a  are  changed,  la  from  9  to  3,  /a  from 
7  to  1.  HarTnonic  intervals  are  indicated  by  numbers 
specifying  the  exact  relation  of  a  tone  to  its  har- 
monic root:  such  are  the  numbers  over  the  above 
chords.  C/iord-intervals  are  computed  from  chord- 
roots.  Since  any  tone,  that  is,  any  component  of  a 
harmony  may  be  a  chord-root  it  follows  that  chord- 
roots  and  chord-intervals  are  sometimes  harmonic 
roots   and   harmonic   intervals  and   sometimes  not, 


ACCENT  AND  REGNANT  HARMONY         137 

wherefore  no  chord  can  be  understood  except  through 
harmonic  analysis.  Above  at  a)  the  chord-intervals 
of  vii°7  are  root,  minor  third,  diminished  fifth,  minor 
seventh,  while  the  harmonic  intervals  of  the  same 
tones  are  respectively  major  third,  pure  fifth,  minor 
seventh,  major  ninth.  These  chord-intervals  generate 
discord  between  feeling  and  thought  while  the  har- 
monic numbers  unite  feeling  and  thought  in  complete 
concord :  the  former  are  arbitrary  and  false,  the  latter 
are  self-asserted,  unalterable  and  true.  At  h)  and 
c)  the  chord-intervals  and  harmonic  intervals  agree, 
but  this  agreement  becomes  less  and  less  frequent 
the  further  we  penetrate  into  the  domain  of  chords, 
and  therefore  the  call  for  exact  harmonic  analysis  will 
grow  correspondingly  more  and  more  frequent. 

Intervals  are  further  to  be  distinguished  under  two 
heads:  1.  Intervals  of  concurrence.  2.  Intervals  of 
succession.  To  the  first  belong  the  intervals  formed 
by  the  concurring  components  of  a  tone's  harmonic 
thread  and  of  a  chord.  To  the  second  belong  all 
steps  from  one  tone's  harmonic  thread  to  another 
and  from  one  chord  to  another;  in  short,  all  steps  in 
one  voice  and  in  combined  voices.  Here  is  an  exam- 
ple in  one  voice :  — 

351535513      ^31 


i 


IV  I     v^ 

In  moving  from  one  of  these  tones  to  another  the 
steps  are  major  second,  major  second,  pure  fourth, 
major  second,  minor  third,  and  so  on.     Thus   we 


138 


THE  NATURE  OF  MUSIC 


observe  the  above  intervals  in  the  ordinary  sense  of 
length  of  steps,  to  perceive  and  know  which  is  to 
perceive  and  know  very  little  since  such  interval- 
steps  give  us  no  intelligence  whatever  of  what  is  most 
essential,  namely,  the  inherent  harmony  of  each  of 
the  two  tones  in  such  a  step.  The  essential  thing  to 
perceive  and  know  is  that  in  moving  from  the  first  to 
the  second  tone  we  are  stepping  from  mi  the  third 
of  one  harmony  to  re  the  fifth  of  another  harmony,  for 
this  includes  the  perception  of  the  whole  step  or 
major  second  from  mi  to  re  and  the  knowledge  of  the 
length  of  this  step  is  but  secondary  and  supplementary 
to  that  of  the  two  harmonies.  This  is  true  of  all  steps 
in  one  voice,  true  likewise  of  the  steps  of  each  chord- 
voice  as  we  move  from  chord  to  chord.  Equally  if 
not  more  important  is  the  necessity  to  discriminate 
between  the  intervals  formed  by  any  two  tones  in 
a  given  chord  and  the  harmonic  report  of  each  of  the 
two  tones.  Two  voices  will  suffice  to  illustrate  this 
point  as  follows:  — 

S*^       55       1311515 
153''3''353'^3 


^i 


^ 


B 


r 
I 


v^  I    V7   I    Y^  I    V    I     y^  I 

The  intervals  of  these  combinations  or  chords  are 
as  follows:  major  third,  minor  third,  minor  third, 
major  sixth,  minor  sixth,  augmented  fourth,  minor 
sixth,  pure  fourth,  minor  third,  major  second,  minor 
third.  With  these  intervals  compare  the  superscribed 
harmonic  reports  and  note  that  the  first  chord  is  the 


ACCENT  AND  REGNANT  HARMONY         139 

only  one  in  which  the  interval-numbers  and  the  har- 
monic report  do  not  conflict.  Numbers  are  used  for 
so  many  and  various  purposes  in  music  that  we  cannot 
wonder  that  students  are  so  easily  confused.  Since 
the  harmonic  numbers  alone  accord  with  the  common 
feeling  and  perception  of  relations  they  should  bring 
some  order  out  of  this  confusion.  The  term  minor 
appears  over  and  over  again  in  the  above  description 
of  intervals  notwithstanding  the  fact  that  the  entire 
example  does  not  contain  a  single  minor  harmony, 
percept  and  concept.  Why  not  like  the  Germans 
use  the  terms  major  and  minor  exclusively  in  connec- 
tion with  modes  and  harmonies?  Why  not,  as  they 
do,  describe  major  intervals  as  great  (gross),  minor 
intervals  as  small  (klein)  f  How  much  simpler, 
clearer,  more  sensible  and  practical  to  describe  the 
above  intervals  thus:  great  third,  small  third,  small 
third,  great  sixth,  small  sixth,  and  so  on.  This 
German  custom  will  henceforth  be  adopted  in  these 
pages. 

We  have  seen  that  one-voice  harmony  is  self-asser- 
tive, that  in  one  voice  the  harmonies  are  always  com- 
plete,  that  is,  single  tones  give  rise  to  harmonic  threads 
of  three,  four  and  five  components.  Chords  are  selec- 
tive combinations  of  tones  and  may  represent  a  har- 
mony incompletely  as  well  as  completely :  thus  a  triad 
may  be  represented  by  a  combination  of  two  or  all 
three  of  its  components ;  a  seventh-chord  by  two,  three 
or  all  four  of  its  components;  a  ninth-chord  by  two, 
three,  four  or  all  five  of  its  components.  Briefly,  one- 
voice  harmony  is  assertive  and  its  harmonic  forms 
are  complete;  chord-forms  are  selective  and  may  be 


140  THE  NATURE  OF  MUSIC 

complete  or  incomplete.  A  second  voice  always 
implies  a  first  voice  to  which  a  second  voice  is  added 
and  this  second  or  added  voice  is  always  selective. 
The  original  guide  in  the  selection  of  one  or  more 
added  voices  is  the  concomitant  harmony  or  harmonic 
thread  of  each  tone  in  the  first  voice,  and  this  first 
voice  is  always  the  dominating  voice*  or  melody  to 
which  all  added  voices  are  subordinate.  In  short,  the 
dominating  voice  is  the  melody  the  concomitant 
harmonies  of  which  in  every  concrete  case  are  this 
or  that  series  as  generated  by  the  specific  relations  of 
its  tones.  When  Wagner  states  that  his  melodies  and 
their  harmonies  arise  in  his  mind  simultaneously  he 
calls  our  attention  to  a  great  truth,  namely,  the 
indissoluble  unity  of  melody  and  harmony.  Had 
Wagner  developed  this  idea  theoretically  his  psycho- 
logy would  doubtless  have  led  him  to  discover  original 
self-assertive  harmony  in  one  voice.  The  influence 
of  the  dominating  voice  not  alone  on  the  selection  of 
harmony,  but  also  upon  conception  and  expression, 
will  be  more  fully  dealt  with  in  the  chapters  on  poly- 
phony and  chords.  The  three  one-voice  harmonies 
I,  Vy  and  V9  have  given  us  the  complete  triad,  com- 
plete seventh-chord  and  complete  ninth-chord.  These , 
three  are  the  prototypes  of  all  like  chords.  From 
common  feeling  of  harmony  in  one  voice  we  have 
derived  the  principle  of  chord-building  which  is  to 
superadd  a  third,  fifth,  seventh  and  ninth  to  a 
fundamental  tone  which  is  the  chord-root.  We  have 
seen  that  I,  V  and  IV  are  the  only  three-tone  diatonic 
harmonies  which  assert  themselves  in  one  voice  in 
Major.    But  in  chord-building,  triads,  seventh-chords 


ACCENT  AND  REGNANT  HARMONY         141 

and  ninth-chords  may  be  and  are  produced  on  each 
of  the  seven  diatonics  and  are  incorporated  in  the 
Major  mode.  All  these  chords  also  appear  in  the 
Minor  mode  in  completely  changed  relations  and 
with  completely  transmuted  harmonic  reports  of  their 
components  directly  caused  by  the  changed  relations. 
In  short,  a  given  chord  is  one  thing  in  Major  and 
quite  another  thing  in  Minor,  as  we  shall  see.  Mean- 
while we  here  note  that  chords  like  one-voice  har- 
monies fall  into  two  divisions:  consonances  and 
dissonances.  Each  of  these  two  divisions  of  chords 
subdivides  into  two  varieties,  namely,  simple  and 
compound  chords.  A  simple  chord  is  built  of  the 
components  of  one  harmony:  such  are  all  the  chords 
thus  far  derived  and  presented  on  a  previous  page. 
A  compound  chord  is  built  of  the  components  of  two 
or  more  harmonies:  this  variety  of  chord  will  be 
explained  in  the  proper  place.  In  chorded  music 
regnant  harmony  and  byharmony  become  regnant 
chord  and  by  chord.  The  subject  of  chords  is  resumed 
in  the  next  chapter. 

40.    The  Tone-Region,     Its  Diatonic  Scales 

Each  of  music's  seven  octaves  repeats  the  same 
series  or  scale  of  tones,  and  forms  the  nucleus  of  a 
tone-region.  The  tones  of  all  regions  are  connected 
by  their  harmonic  threads,  and  the  relative  pitch  of 
each  tone  is  due  to  harmonic  relation.  The  seven 
diatonics  constitute  the  first  group  of  tones  that  was 
discovered,  expressed  and  exploited,  and  the  causes 
and  order  of  their  genesis  have  been  explained.  The 
tone-region  shows  the  natural  juxtaposition  of  tones. 


142  THE  NATURE  OF  MUSIC 

Regnant  I  being  the  first  harmony,  do  being  the  root 
of  this  harmony  and  the  original  meloharmonie  point 
of  repose  which  we  call  the  Tonic,  it  follows  that  do 
is  the  original  centre  of  the  tone-region,  as  follows :  — 


sol  —  la  —  ti  ^  Do  —  re  —  mi  ^  f  a 


V  I  IV 

Here  the  seven  diatonics  form  a  scale  of  two 
conjunct  tetrachords.  The  Tonic  do  is  the  common 
tone  and  common  centre  of  the  two.  A  tetrachord 
is  a  scale  of  four  tones.  The  above  dashes  ( — )  and 
curves  (w)  indicate  respectively  whole  steps  and 
half  steps,  and  show  that  the  two  above  tetrachords 

have  the  same  form,  namely, ^-^.     This  scale  of 

seven  tones  and  conjunct  tetrachords  I  have  named 
the  septonate.*  The  septonate  is  the  nucleus  of  the 
tone-region.  What  evidence  is  there  that  do  the 
Tonic  is  the  original  centre  of  the  tone-region  ?  The 
incontrovertible  evidence  is  adduced  from  harmony 
briefly  as  follows:  — 

The  cadence  of  V  rises  or  resolves  upward  into  I; 
the  cadence  of  IV  resolves  downward  into  I:  ergo,  I 
lies  between  V  and  IV.  This  septonal  nucleus  of  the 
tone-region  besides  being  the  index  of  meloharmonie 
resolution  is  also  the  index  of  progression.  For 
example,  from  V  to  IV  progress  upward,  from  IV  to 
V  progress  downward.  What  is  true  of  these  har- 
monies is  true  of  the  corresponding  chords.  From 
the  intuitive  feeling  of  these  one-voice  self-assertive 
resolutions  and  progressions  the  rules  for  treating  the 
corresponding  chords  in  corresponding  relations  and 


ACCENT  AND  REGNANT  HARMONY        143 


for  treating  all  other  chords  in  similar  relations  in 
the  same  way  have  been  derived  by  induction. 

The  diatonics  form  a  scale  of  eight  tones  in  which 
the  same  two  tetrachords  are  disjunct.  This  scale 
proceeds  from  the  Tonic-centre  of  one  tone-region  to 
the  Tonic-centre  of  a  contiguous  region;  in  it  the 
two  Tonics  form  lower  and  upper  terminals.  This 
our  familiar  Major  scale  is  as  follows :  — 


Do  — re  — mi  -^fa  — sol  —  la  —  ti       Do 


I  IV    V  I 

A  consonant  thread  of  harmony  extends  throughout 
the  range  of  pitch  and  connects  all  its  components  in 
all  regions.  Of  these  threads  I  is  the  genus  and 
original,  V  and  IV  are  relative.  In  the  following 
illustration  the  arrows  indicate  the  whole  range  of 
pitch. 


I— ^1  — ^iV 


i 


i 


The  thread  of  the  dissonant  genus  V9  extends  from 
one  region  into  the  next,  and  in  each  octave  one  such 
thread  intersects  another  thus:  — 


144  THE  NATURE  OF  MUSIC 

At  each  intersection  four  components  of  V9  form 
the  tetrachord  of  three  consecutive  whole  steps  known 
as  the  tritonus,  as  follows :  — 

•^      1      9     3 

fa  —  sol  —  la  —  ti 
—  ^^ 

A  few  of  the  dissonant  chords  formed  by  combining 
these  tones  are  next  given  in  close  and  open  positions. 

9 

3       3 

1       -^         9       1       9         3        9        9       '^ 

119       19        3        11 

7  -g?- 


i 


i 


s?^        f>       i-g^ 


25^ 


-^^ ^- 


^^ TSr 


V,  V9 

Here  observe  in  passing  that  the  tri tonus  is  the 
only  tetrachord  whose  four  tones  are  components  of 
one  harmony  and  together  form  a  simple  chord  of 
the  dissonant  type. 

A  septonate  is  named  by  its  central  tone:  thus  the 
above  septonate  is  the  Tonic-septonate.  A  diatonic 
scale  of  eight  tones  is  named  by  its  terminal:  the 
above  octonal  scale  is  likewise  a  Tonic-scale.  Each 
of  the  seven  diatonics  may  appear  as  a  septonal 
centre  of  two  conjunct  tetrachords  and  the  octonal 
terminal  of  two  disjunct  tetrachords,  and  each  such 
scale  like  that  of  the  Tonic  is  named  by  its  septonal 
centre  and  octonal  terminal.  Thus  sol  the  Dominant, 
fa  the  Subdominant,  mi  the  Mediant,  la  the  Sub- 
mediant,  re  the  Supertonic,  ti  the  Subtonic,  each  of 
these  may  be  the  septonal  centre  and  the  octonal 
terminal  and,  as  these  syllables  and  names  imply,  all 


ACCENT  AND  REGNANT  HARMONY        145 

these  scales  are  related  to  the  original  scales  of  the 
Tonic.  In  these  scales  there  are  four  forms  of  tetra- 
chords  as  the  subjoined  groups  of  symbols  of  whole 
and  half  steps  show. 

1.  2.  3.  4. 

I---I    I---I    I---I    I---I 

I  here  present  the  septonal  conjunct  forms  of  these 

scales.  

''  -^-^  "-^ 

do  —re  —mi  ^s^  Fa  —  sol  —  la  —  ti 


ti^do  —re  —  Mi  ^^fa  —  sol —la 


la  —  ti  v_^  do  —  Re  — mi  -^^fa  —  sol 


Sol—La  —  Ti^^  Do  —Re  —Mi  v^  Fa 


fa  —  sol  —  la  —  Ti  s.^  do  —  re  —  mi 


mi  ^^fa  —  sol  —  La  —  ti  >w^  do  —  re 


re  —  mi  -^^^  fa  —  Sol  —  la  —  ti  s»^  do 

The  above  capitalized  syllables  of  the  central 
Tonic-septonate  and  those  marking  the  centre  of  each 
individual  septonate  form  a  Greek  cross  which  ap- 
positely suggests  the  Greek  modes,  which  I  next  pre- 
sent in  their  octonal  form  of  disjunct  tetrachords. 


^ — & — P5 


-^2 ^ 


La  to  La    Sd  \o  Sd 

Fa  to  Fa   Mi  to  Mi 


i 


146 


THE  NATURE  OF  MUSIC 


g 


■Z7- 


W 


^ sr 


-^—TSr 


SL 


tS* Z?-^ 


■^—z^- 


Be 


to 


iJe    Do 


to 


2)0 


i 


Ti 


^ — ^ — ^ 
to 


Ti 


In  three  of  these  septonal  and  corresponding 
octonal  scales  the  two  tetrachords  in  each  have  the 
same  form:  in  both  Tonic-scales  both   tetrachords 

have  this  form, ^^i  in  both  Supertonic-scales 

they  have  this  form,  —  -^  — :  in  both  Mediant-scales 

they  have  this  form,  ^^ .     In  each  of  the  other 

septonal  and  octonal  scales  the  forms  of  the  two 
tetrachords  differ,  as  the  examples  show.  The  appear- 
ance of  these  tetrachords  in  all  music  is  most  common. 
For  illustrations  the  reader  is  referred  to  Bach's  first 
** Invention"  in  two  voices  and  the  principal  theme 
of  Wagner's  "Meistersinger."  All  the  above  tetra- 
chords will  be  found  in  the  following  quotation  from 
Beethoven's  E  flat  Concerto:  — 


In  his  book  on  "The  Music  of  Antiquity"  Gevaert 
has  extricated  the  Greek  modes,  their  identity  and 


ACCENT  AND  REGNANT  HARMONY         147 

names  and  their  true  connection  with  the  church- 
modes  from  a  state  of  greatest  confusion.  My  chief 
purpose  in  bringing  forward  these  ancient  modes  at 
this  juncture  is  to  point  out  the  fact  that  they  all  lie 
in  and  form  part  and  parcel  of  our  modern  tone- 
system.  Thus  far  the  attempts  to  harmonize  the  few 
extant  specimens  of  Greek  melodies  in  accordance 
with  the  arbitrary  rules  of  chord-harmony  appear 
not  to  have  been  successful  or  satisfactory.  The 
same  may  be  said  of  the  harmonizations  of  Gregorian 
and  Ambrosian  melodies.  Indeed,  the  consensus  of 
opinion  seems  to  be  that  the  addition  of  chords 
distorts  and  destroys  the  inherent  character,  power 
and  simple  beauty  of  such  melodies,  and  that  they 
should  therefore  be  left  unharmonized.  This  dis- 
approval of  adding  chords  to  such  music,  which 
originated  in  one  voice,  gains  significance  when  we 
consider  on  the  one  hand  that  this  disapproval 
springs  directly  from  the  common  harmonic  sense  and 
is  therefore  a  common  report  of  common  music- 
feeling  while  on  the  other  hand  it  is  natural  that  no 
two  investigators  should  agree  on  any  one  series  of 
chords  for  a  given  melody.  And  why.?  Simply 
because  chord-harmony  is  purely  selective  and  always 
the  expression  of  personal  judgment  and  taste.  But 
original  harmony  in  one  voice  and  its  common  reports 
place  the  subject  of  the  music  of  antiquity  and  its 
harmonization  on  a  new  basis  and  in  a  new  light. 
The  Greeks  had  no  multi-voice  harmony,  but  they 
had  one-voice  harmony  although  they  did  not  know 
it;  they  had  no  idea  of  harmony  in  our  sense  of 
chords,  but  they  had  the  harmonic  sense  and  applied 


148  THE  NATURE  OF  MUSIC 

the  term  harmonies  to  the  tones  composing  their 
modes.  Their  possession  of  the  common  harmonic 
sense  is  proved  by  the  fact  that  on  one  hand  they 
perceived  that  certain  tones  tended  to  others  (sense 
of  dissonance),  and  on  the  other  hand  that  a  certain 
tone  was  final,  the  tone  to  stop  on  (sense  of  conso- 
nance). When  Aristoxenus  describes  the  sudden 
transition  from  the  pitch  of  one  tone  to  that  of  another 
as  **  the  topical  motion  from  the  repose  of  one  tone 
to  that  of  another"  he  is  unconsciously  expressing 
his  intuitive  sense  of  one-voice  harmony.  His  defini- 
tion of  rhythm  would  indeed  be  a  credit  to  twentieth- 
century  text-books  and  encyclopaedias.*  If  not  his 
intuitive  harmonic  sense,  what  was  it  that  caused 
Aristides,  pupil  of  Aristotle,  to  make  these  queries, 
**  Why  is  it  that  when  I  change  the  mese  (middle  tone) 
all  the  other  tones  are  wrong;  why  when  I  change  one 
of  the  other  tones,  that  one  alone  is  wrong.?"  Such 
evidence  that  the  Greeks  possessed  the  harmonic 
sense  might  be  multiplied  indefinitely.  Books  which 
shall  embody  the  common  reports  of  original  harmony 
on  Greek,  ecclesiastical,  in  short,  on  all  one-voice 
music,  remain  to  be  written,  a  life-work  not  for  one, 
but  for  many.  In  another  place  analyses  of  several 
Greek  melodies  and  Gregorian  chants  will  be  pre- 
sented. Certain  types  of  music  are  spoken  of  by 
historians  and  theorists  as  music  without  harmony 
and  music  without  rhythm.  As  I  have  said  and 
shall  reiterate  over  and  over  again,  melody  without 
harmony  and  melody  without  rhythm  never  existed. 
The  concomitant  harmony  of  melody  being  self- 
assertive  and  its  reports  being  common  it  follows 


ACCENT  AND  REGNANT  HARMONY        149 

that  every  melody  ancient  or  modern  is  the  messen- 
ger of  common  harmonic  reports.  The  rhythm  of 
ancient  melodies  may  be  traced  in  all  cases  where  the 
melody  is  accompanied  by  a  text,  for  the  alternating 
syllabic  accents  of  the  text  discover  the  heavy  recur- 
ring accents  which  are  at  once  the  measure-accents 
and  the  efficient  accents  of  regnant  harmony.  In 
harmonizing  the  melodies  of  antiquity  the  selection 
of  chords  should  be  made  to  conform  with  the 
concomitant  harmonies  which  each  such  melody  itself 
asserts.  Harmonizations  so  selected  would  emphasize 
and  enhance  rather  than  distort  and  destroy  the  true 
nature,  beauty  and  effect  of  such  melodies,  would 
strengthen  rather  than  weaken  them,  and  would  cir- 
cumvent the  personal  equation.  Original  harmony 
in  one  voice  therefore  not  only  empowers  us  to  per- 
ceive the  concomitant  harmonies  of  a  Greek  melody 
and  Gregorian  chant,  but  empowers  us  to  feel  a  Greek 
melody  as  the  Greeks  felt  it,  to  feel  a  Gregorian  chant 
as  Gregory  himself  felt  it. 

41.    Musical  Moments.     Power  and  Originality 
of  Music 

While  thinking,  expressing  or  listening  to  music 
as  we  proceed  rhythmically  from  tone  to  tone,  from 
moment  to  moment,  the  inner  consciousness  unites 
with,  our  whole  being  is  merged  in  the  flight  of  time 
itself;  self-consciousness  is  annihilated,  the  spirit  is 
liberated,  our  self-surrender  is  complete.  During 
these  musical  moments  we  are  dominated  and  swept 
onward  by  music's  elemental  forces  and  shaping 
principle;  we  are  ever  in  the  present,  now — here^ 


150  THE  NATURE  OF  MUSIC 

now — here.  Now  denotes  time  (rhythm),  here  denotes 
space  (harmony) :  now — here  connotes  composite  form 
and  relation  in  time  and  space,  the  united  harmonies 
of  rhythm  and  tone,  the  musical  moment.  This 
complete  obliteration  from  consciousness  of  all  other 
ideas  and  mental  processes,  this  enthralling  concen- 
tration of  the  attending  inner  consciousness  upon 
the  musical  moment,  the  ever  present,  is  the  secret 
of  music's  great,  perhaps  greatest,  power.  Whatever 
else  this  power  may  be,  at  bottom  it  is  elemental,  it 
inheres  in  the  elements  and  principles  of  music,  a 
field  of  investigation  far  from  being  exhausted,  the 
only  field  free  from  speculation  and  open  to  scientific 
accuracy  of  observation.  The  true  and  the  beautiful 
are  rooted  in,  spring  from  and  are  shaped  by  these 
elements  and  principles,  their  power  is  primarily  due 
to  this  elemental  power,  they  are  vague  and  myste- 
rious in  themselves  yet  nothing  could  be  more  real 
and  potent.  At  least  we  know  that  our  knowledge 
of  the  aesthetic  power  of  music  must  ever  remain 
limited  to  what  we  can  learn  from  its  elemental 
power.  Alike  spell-bound,  liberated  and  uplifted  by 
this  great  power  of  the  musical  moment  are  the 
producing  composer,  the  reproducing  artist  and  the 
contemplating  listener.  The  psychology  of  the  pro- 
ducing composer  is  eloquently  set  forth  by  Wagner 
in  his  essay  on  Beethoven.  The  musical  moment 
of  the  artist  and  listener  will  be  considered  pres- 
ently. 

In  the  universe  of  one  rhythm  struggling  for  and 
maintaining  one  equilibrium  or  harmony  each  motion 
and  moment  are  parts  of  a  correlated  and  equili- 


ACCENT  AND  REGNANT  HARMONY        151 

brating  whole.  Each  moment  in  the  short  space  of 
a  single  human  life  is  a  rhythmic  moment  accentuat- 
ing the  individual  struggle  for  physical,  mental,  social 
and  spiritual  equilibrium  or  harmony.  When  we 
consider  that  music  is  the  direct  language  of  equili- 
brium or  harmony,  and  that  it  directly  presents  the 
universal  message  of  all  the  arts,  we  can  no  longer 
regard  its  universal  power  as  a  mystery  not  to  be 
penetrated  and  wholly  insoluble.  What  choice  or 
will  has  man  to  resist  universal  energy,  rhythm  and 
equilibrium,  universal  form  and  principle  of  form, 
all  of  which  underlie,  are  blended  and  idealized  in 
music  .^^  I  have  pronounced  music  to  be  the  only 
universal  and  only  purely  spiritual  language,  but  it 
is  more;  it  is  the  language  of  liberty  and  freedo^n,  it 
is  a  complete  whole  to  which  nothing  can  be  added, 
from  which  nothing  can  be  taken  away.  Can  you 
add  anything  to  or  take  anything  from  a  tone,  is  not 
a  tone  complete  in  itself.^  Music's  elemental  power 
to  absorb  the  whole  attention  and  to  annul  all  the 
ordinary  conscious  activities  of  thought  and  volition 
is  due  more  to  tone  than  to  rhythm.  Musical 
rhythm  'per  se  does  not  possess  this  power.  Why? 
Because  we  are  so  pervaded  with  this  law  of  motion 
that  we  spontaneously  take  up  an  initial  rhythm, 
remember  it,  repeat  it,  and  therefore  anticipate  it 
without  conscious  effort  of  attention,  in  a  word,  with- 
out knowing  it.  With  tap  of  hand  or  foot  we  often 
unconsciously  take  up  any  pronounced  rhythm  in 
our  environment  and  sharply  mark  the  recurring 
accents  to  which  we  sometimes  hum  an  improvised 
air.     So  fixed  is  the  innate  rhythmic  habit  of  pre- 


152  THE  NATURE  OF  MUSIC 

serving  the  equilibrium  from  moment  to  moment, 
so  keen  the  sense  of  keeping  time  or  balance  that  our 
anticipation  of  the  recurring  periods  of  music  is  per- 
fectly definite;  because  we  feel  what  is  coming  we  do 
not  stop  to  think  about  it.  This  is  why  rhythm  per  se 
has  not  the  power  of  concentrating  the  whole  atten- 
tion and  does  not  necessarily  even  attract  the  attention. 
However,  all  this  is  changed  when  tone,  the  living  and 
original  voice  of  music,  unites  with  rhythm;  it  is 
then  that  the  elemental  power  asserts  itself  and  holds 
the  attention.  Each  tone  in  a  musical  series  com- 
mands the  entire  attention;  not  one  progression  or 
resolution  if  unperceived  that  does  not  break  the 
thread  of  connection,  that  does  not  mar  our  sense  of 
the  whole..  Let  the  music  be  familiar  or  unfamiliar, 
in  either  case  absolute  attention  upon  each  tone  is  a 
necessity;  the  momentary  relation  of  each  tone  must 
be  felt  by  the  artist  else  he  cannot  express  it,  by  the 
listener  else  he  loses  the  connection.  In  unfamiliar 
music  it  is  obvious  that  the  listener  cannot  anticipate 
progressions  or  even  resolutions,  but  even  in  familiar 
music  where  he  does  anticipate  them,  and  where  he 
anticipates  whole  phrases,  sentences  and  paragraphs, 
nevertheless,  he  is  compelled  to  rivet  his  attention 
upon  each  tone -moment,  now — ^here,  now — ^here. 
This  rapt  attention  upon  the  musical  moment  is  not 
the  result  of  any  conscious  or  voluntary  effort,  it  is  the 
direct  effect  of  music's  elemental  power,  the  power 
of  tone-rhythm.  The  artist  expresses  the  musical 
moment  as  he  feels  it  then  and  there.  He  has  grouped 
the  series  of  moments  in  a  composition  into  motives, 
phrases,  sentences,  paragraphs;  he  has  correlated  and 


ACCENT  AND  REGNANT  HARMONY         153 

unified  all  these  parts  into  a  great  whole :  yet  when  he 
produces  his  work  his  consciousness  is  concentrated 
upon  each  tone-moment,  now — here,  now — here.  It 
is  precisely  because  the  artist  has  conceived  the  whole 
in  all  its  parts,  precisely  because  he  knows  and 
anticipates  each  motive,  phrase,  sentence  and  para- 
graph, that  he  is  able  to  concentrate  his  attention 
upon  each  moment,  that  he  can  express  then  and 
there  what  he  feels  then  and  there.  Certainly  the 
artist  cannot  express  now  when  he  is  thinking  of  by 
and  by.  Observe  your  pupil  who  while  playing  on 
page  1  is  disturbed  by  the  consciousness  of  an 
approaching  difficulty  on  page  2.  It  is  plain  that 
the  thought  of  by  and  by  is  effectually  musicidal  to 
the  momentary  expression  of  now.  In  each  tone  of 
a  melody  there  is  a  balance  of  the  united  harmonies 
of  time  (rhythm)  and  space  (tone)  to  be  perceived, 
which  if  unperceived  then  and  there  are  lost  forever. 
Common  music-feeling  in  which  this  union  of  har- 
monies originated,  whence  it  emanates,  to  which 
it  alone  appeals  and  is  directed,  is  therefore  at  once 
the  originator,  the  transmitter  and  receiver  of  the 
rhythmo-harmonic  voice  of  music,  melody.  The 
psychology  of  music's  elemental  power  presents  an- 
other chapter,  the  subject  of  which  is  the  operation 
of  the  law  of  gravitation  in  the  domain  of  feeling  and 
thought.  Light  rhythm-periods  tend  and  resolve  into 
heavy  rhythm-periods,  which  are  rhythmic  centres 
of  gravity;  dissonances  tend  and  resolve  into  conso- 
nances, which  are  harmonic  centres  of  gravity :  in  both, 
this  tendency  to  resolve  is  attraction  into  equilibrium. 
Having   thus   roughly   explained   music's   elemental 


154  THE  NATURE  OF  MUSIC 

power  as  concentrated  in  the  musical  moment  we  will 
next  briefly  consider  music's  originality  and  unique 
position  as  an  art. 

Tone  has  just  been  described  as  a  complete  whole 
to  which  nothing  can  be  added,  from  which  nothing 
can  be  taken  away.  Tone  is  unique,  therefore 
original;  there  is  nothing  like  it  or  comparable  to  it 
in  the  entire  realm  of  expression  in  which  it  has  but 
one  rival,  speech.  But  the  spoken  word  describes, 
defines,  voices  something  not  itself  and  is  a  means 
to  an  end,  while  tone  directly  voices  itself,  only  itself, 
and  is  at  once  both  means  and  end.  Again,  the 
spoken  word  has  a  specific  meaning,  a  meaning  put 
into  it,  while  tone  has  a  universal  meaning,  a  meaning 
not  put  in  but  inherent,  which  is  harmony.  Tone  is 
directly  presentative ;  tone-language  ^presents  itself  and 
nothing  else;  it  does  not  and  cannot  represent  or 
misrepresent,  nor  can  it  be  represented  in  artificial 
substances  or  forms.  Music  is  idea  in  tones,  no 
more,  no  less.  Tone-rhythm  embodies  and  presents 
the  music-idea,  nothing  else.  When  we  contem- 
plate music  we  contemplate  the  reality,  the  thing 
itself,  music.  A  statue  or  portrait  of  a  man  is  a 
statue  or  a  portrait,  but  not  the  reality,  the  thing 
itself,  a  man.  Tone-rhythm  is  substance  and  form 
in  one.  Substance  and  form  of  what.?  Of  the 
music-idea,  which  is  melody,  the  composite  of  rhythm 
and  harmony.  Unlike  the  substances  which  the 
other  arts  change  from  their  original  form  into  some- 
thing else,  into  a  building,  a  statue,  a  painting,  the 
substance  of  music  permanently  preserves  its  original 
form,  is  immutable,  cannot  be  shaped  into  anything 


ACCENT  AND  REGNANT  HARMONY         155 

but  music.  The  subject  of  music  or  the  music-idea 
is  always  melody,  the  substance  and  form  of  music 
is  always  tone-rhythm,  therefore  in  music  the  subject 
and  the  substance  are  not  only  always  united,  but 
neither  exists  independently  of  the  other,  the  two 
cannot  be  sundered.  Great  and  greatest  music  re- 
quires no  fuller  titles  than  Melody  in  A,  Sonata  in  B, 
Symphony  in  C.  This  perfect  union  and  insepara- 
bility of  subject,  substance  and  form  in  the  music-idea 
or  melody  which  directly  presents  itself  and  which 
cannot  present  something  not  itself,  at  once  points 
out  the  originality  of  music,  its  unique  position  as  an 
art  and  distinguishes  music  from  the  other  arts.  I 
have  just  defined  music  as  idea  in  tone.  More  wide- 
spread than  one  might  suppose  is  the  narrow  view 
which  limits  the  idea  to  that  which  can  be  expressed 
in  words.  Were  this  true  the  inner  psychical  world 
of  ideas  would  be  deprived  of  much  besides  music. 
An  idea  is  that  which  conveys  complete  sense  to  the 
mind  no  matter  what  its  peculiar  form  or  vehicle  may 
be,  no  matter  what  sense  or  combination  of  senses  it 
appeals  to.  The  mind's  wealth  of  ideas  is  limited 
only  by  the  number  of  forms  or  vehicles  in  which  to 
embody  and  express  ideas,  and  no  one  form  of  idea 
has  a  perfect  equivalent  in  any  other  form.  There 
is  no  equivalent  in  words  for  an  idea  in  tones  and  vice 
versa.  A  beautiful  melody  is  a  perfect  idea  in  tones 
just  as  a  beautiful  poem  is  a  perfect  idea  in  words. 
Each  is  perfect  of  its  kind,  the  one  no  more  so  than 
the  other,  perfection  being  absolute  and  not  relative. 
We  may  compare  the  psychology  of  the  two  ideas  and 
their  relative  power,  not  their  truth  and  beauty,  for 


156  THE  NATURE  OF  MUSIC 

the  true  and  the  beautiful  are  ever  perfect.  How 
vain,  hopeless,  even  absurd  is  the  seeking  of  equivalent 
ideas  in  words  for  ideas  in  tones. 

The  language  of  tones  alone  completely  voices  and 
harmonizes  the  composite  inner  experience;  it  is  the 
inner  world  of  harmony  governed  by  the  same  laws 
as  the  outer  world  which  it  mirrors,  it  is  therefore  a 
whole;  universal  harmony  is  its  essential  message, 
universal  harmonization  of  mankind  is  its  essential 
purpose  and  function.  The  composite  inner  experi- 
ence with  its  infinitesimal  number  of  elements  is 
summed  up  in  the  momentary  mood  (Stimmung),  and 
the  most  we  can  say  of  the  ever  changing  mood  is  that 
it  is  now  brighter,  now  darker,  or  now  lighter,  now 
heavier;  that  it  varies  in  the  individual  and  is  not 
the  same  in  any  two  individuals.  Music  attunes  the 
momentary  mood  of  one,  of  all;  here  lies  its  power, 
the  power  of  the  musical  moment.  All  the  other  arts 
share  in  the  universal  message  and  purpose,  but  no 
one  or  combination  of  them  so  pervade  the  inner  life, 
exert  so  great  a  power  or  occupy  so  unique  a  position 
in  the  art-hierarchy  as  does  music.  In  the  drama  we 
note  that  the  other  arts  merge  into,  aid  and  strengthen 
each  other  in  accomplishing  the  essential  purpose  of 
the  drama  which  first  of  all  is  pure  illusion.  But 
music  being  a  whole  and  complete  in  itself  does  not 
and  cannot  merge  with,  be  aided  and  strengthened  by 
the  other  arts.  The  drama  is  illusion,  music  is  reality; 
the  drama  represents,  music  presents.  Drama  and 
music  are  therefore  antitheses,  each  is  most  potent  by 
itself,  each  antagonizes  and  disturbs  the  other  when 
the  two  are  associated,  as  in  the  music-drama.     For 


ACCENT  AND  REGNANT  HARMONY         157 

these  reasons  in  the  main  the  music-drama  is  a  work  of 
hybrid  not  of  pure  art.  Whenever  and  wherever  music 
presents  itself  it  attracts  and  dominates  the  attention. 
In  all  its  associations  with  other  arts  music  refuses  to 
play  a  second  part  and  never  does.  The  composers 
of  songs,  cantatas  and  operas  are  great  and  greatest 
only  when  and  where  their  music  is  great  and  greatest. 
Music-contemplation  is  disturbed  in  the  opera  by  the 
presence  of  scene  and  action,  in  the  cantata  by  the 
implied  scene  and  action  which  the  imagination  must 
supply.  Words  expressive  of  pure  sentiment  alone 
blend  harmoniously  with  music,  and  when  distinctly 
rendered  do  not  disturb  music-contemplation,  where- 
fore as  a  work  of  art  the  song  is  purer  than  either 
cantata  or  opera.  Such  hybrid  art-creations,  while 
they  are  justifiable,  exert  immense  power  and  may 
even  be  called  great,  nevertheless  as  works  of  art 
they  are  not  pure.  As  a  matter  of  course  absolute 
music  is  the  most  pure  and  potent  music.  Pure 
enjoyment  in  music-contemplation  is  grounded  and 
dependent  on  anticipation,  that  is,  on  familiarity  with  a 
composition.  The  greater  this  familiarity  the  greater 
our  enjoyment,  the  keener  our  anticipation  of  each 
musical  moment;  it  is  then  that  we  yield  ourselves 
completely  to  the  power  of  the  musical  moment.  The 
unfamiliar  conduces  to  another  species  of  enjoyment 
during  which  the  mind  maintains  the  attitude  of 
interrogation  as  what  next.^  but  this  is  not  the  true 
mental  attitude  of  complete  receptivity  and  pure 
enjoyment.  Every  public  performance  demonstrates 
that  the  familiar  is  most  enjoyed,  wherefore  two  thirds 
of  a  programme  should  be  made  up  of  familiar  com- 


158  THE  NATURE  OF  MUSIC 

positions.  Great  music  and  the  great  scenes  of 
nature  affect  us  similarly.  Both  stir  us  to  the  core 
and  pervade  us  with  the  sense  of  infinity.  In  the 
contemplation  of  either  we  enjoy,  absorb  and  are 
benefited,  each  according  to  individual  capacity  and 
receptivity,  just  so  much,  no  more,  no  less. 

Owing  to  its  peculiar  elemental  power,  its  complete- 
ness in  and  by  itself,  the  universality  of  its  message 
and  function,  the  indissoluble  unity  of  its  subject, 
substance  and  form  in  melody,  it  is  futile  to  compare 
music  with  the  other  arts.  Architecture  is  often 
chosen  for  this  purpose  of  comparison  because  like 
music  it  is  a  presentative  art,  and  certain  analogies  are 
traced  in  its  static  rhythms  and  harmonies  and  the 
mobile  rhythms  and  harmonies  of  music.  *' Archi- 
tecture is  frozen  music,"  is  a  frequent  quotation.  If 
there  must  be  comparisons  let  them  be  sought  in  the 
myriad  recorded  and  mobile  rhythms  and  harmonies 
of  nature  and  not  in  the  other  arts,  whose  subjects 
are  too  specific  and  definite  and  fix  the  attention 
upon  the  same  single  idea  or  group  of  ideas,  thus 
directing  thought  and  feeling  into  the  same  definite 
channels.  There  is  however  a  broad  common  ground 
which  music  shares  with  all  the  arts.  Each  art,  music 
included,  has  its  peculiar  form  or  vehicle  of  expression 
in  which  each  in  its  own  way  embodies  human  thought 
and  feeling.  All  art  is  self-expression,  and  every  art- 
work springs  from  the  imagination.  But  the  building, 
statue,  painting  which  we  behold  are  finished  per- 
formances; each  stands  before  us  in  its  entirety;  each 
has  been  produced  once  for  all  time;  each  time  we 
look  at  it  we  behold  the  same  performance;  each  such 


ACCENT  AND  REGNANT  HARMONY        159 

work  may  be  contemplated  at  leisure;  we  may- 
observe  its  points  in  any  order  we  please  and  may 
discuss  them  with  a  companion  without  disturbing 
the  moments  of  contemplation.  None  of  these  par- 
ticulars apply  to  music.  The  composer's  original  and 
finished  creation  is  a  book  of  symbols  comparable  with 
the  plans  and  specifications  of  the  architect.  True 
the  musician  may  read  the  book  and  hear  the  music 
in  the  way  that  Carlyle  preferred  to  see  plays,  "in 
the  theatre  under  my  hat."  But  the  music- work  to 
be  contemplated  by  the  listener  must  be  performed, 
not  reproduced,  but  actually  and  audibly  produced; 
each  and  every  hearing  involves  a  fresh  and  indepen- 
dent production.  No  artist,  no  conductor  can  exactly 
duplicate  a  previous  production;  each  is  new,  indi- 
vidual. A  music-work  is  produced  then  and  there 
and  contemplated  then  and  there  on  the  spot;  now 
it  begins,  now  it  is  ended  and  ended  forever,  it  has 
passed  into  eternity  along  with  the  moments  during 
which  it  held  artist  and  listener  united  by  its  magical 
spell,  a  mere  evanescing  memory  to  look  back  upon 
and  talk  about.  Not  only  are  the  moments  of  pro- 
duction and  contemplation  concurrent,  not  only  do 
they  begin  and  end  together,  but  they  concentrate  the 
attention  of  both  artist  and  listener  upon  one  and  the 
same  idea;  their  duration  is  prescribed  and  limited; 
there  is  no  looking  backward  until  the  final  harmony 
has  ceased  to  vibrate.  Artist,  it  is  difficult  to  determine 
which  is  the  greatest,  your  responsibility,  your  power, 
or  your  privilege.  Your  responsibility  is  great,  stand- 
ing as  you  do  between  the  masters  whose  creations  it 
is  your  power  and  privilege  to  recreate  and  your 


leo  THE  NATUEE  OF  MUSIC 

fellow  man  to  whom  you  interpret  these  creations. 
Your  responsibility  to  the  master-genius  is  twofold: 
first  of  all,  because  the  message  of  music  is  universal; 
next,  because  the  universal  message  embodied  in 
great  music  is  the  quintessence  of  an  integral  portion 
of  its  creator's  inner  life,  of  his  experience  of  universal 
experience,  for  which  he  demands  a  corresponding 
integral  portion  of  your  inner  life  and  experience,  — ■ 
life  for  life,  heart-beat  for  heart-beat,  a  whole  for  a 
whole,  and  all  this  for  each  and  every  performance. 
Your  responsibility  is  not  lessened  in  that  your 
performance  is  not  handed  down  to  posterity  like 
a  building,  statue  and  painting  for  deliberate  con- 
templation and  for  critical  essay  and  assay.  Yours  is 
but  a  moment,  a  unique  moment  in  infinite  time; 
yours  is  a  unique  power  and  privilege  exerted  at  the 
musical  moment  when  your  heart-beat  is  merged 
with  the  heart-beat  of  hundreds,  even  thousands  of 
your  fellow  men  in  one  harmonious  rhythm,  **im 
Ganzen,  Guten,  Schoenen."  Worthy  are  those  who 
do  not  shirk  the  responsibility,  who  do  not  abuse  the 
power  and  the  privilege. 

42.    Subrhythm  and  Rhythm-Expansion.     Music's 
Classic  Form 

The  term  period  here  used  only  in  connection  with 
rhythm  applies  to  rhythm-waves  of  every  form  and 
length.  There  are  beat-periods,  subbeat-periods, 
measure-periods,  periods  of  two  and  four  measures,  of 
three  and  six,  of  eight  and  twelve  measures,  and  so  on. 
A  beat-period  may  be  divided  and  subdivided  into 
shorter  and  shorter  waves  or  periods;  a  measure- 


ACCENT  AND  REGNANT  HARMONY         161 

period  may  be  expanded  into  longer  and  longer  waves 
or  periods  and  the  form  of  a  wave  or  period  may  be 
regular  or  irregular  while  every  form  is  reducible  into 
the  elementary  rhythm-numbers  2  and  3.  Equili- 
brium, the  shaping  principle,  requires  a  wave  of  one 
length  to  be  followed  and  balanced  by  another  wave 
of  the  same  length.  A  long  period  or  great  wave  is  a 
balanced  composite  of  successively  shorter  and  shorter 
balanced  periods  or  waves  whose  relative  lengths  and 
intensities  are  equal  divisions  and  subdivisions  of  the 
whole,  the  balance  of  each  being  relative  to  that  of 
all  the  others  in  the  balanced  whole  in  accordance 
with  the  inherent  principle  of  form.  Among  all  these 
waves  or  periods  there  is  one  which  is  at  once  the 
characteristic  and  fundamental  rhythm  inherent  in 
and  reported  by  every  phrase  of  melody.  This 
foundation-period,  the  predominating  and  character- 
istic pulse  of  music-thought  and  feeling  I  name  the 
suhrhythm.  The  symbol  of  the  subrhythm  is  the 
measure.  When  two-pulse  the  subrhythm  is  written 
in  dual  measure;  when  three-pulse,  in  triple  measure. 
The  subrhythm  is  the  thing  itself,  the  basic  rhythm- 
idea,  while  the  measure  is  only  its  symbol.  Since 
the  names  of  things  and  those  of  their  symbols  are  not 
interchangeable,  and  since  we  possess  no  term  for 
what  is  here  designated  as  subrhythm,  I  do  not  hesitate 
to  add  this  term  to  our  overstocked  nomenclature. 
Periods  shorter  than  the  subrhythm  play  upon  the 
subrhythm,  they  present  the  play  of  rhythm  upon 
rhythm.  Periods  longer  than  the  subrhythm  are  ex- 
pansions of  the  subrhythm  first  into  phrases,  next 
into  groups  of  phrases,  next  into  groups  of  groups  of 


162 


THE  NATURE  OF  MUSIC 


phrases.     In  the  following  illustration  the  forms  of 
all  the  periods  are  dual. 


3    13  913    13   91313  515    13 


^jfM-'Mf-^^-nf-htj;  r  iJ  f  If  Ji 


IV  IV  I        IV      VI 

In  their  relative  order  from  shorter  to  longer  the 
above  wave-lines  indicate  respectively  beat-periods, 
measure-periods  (subrhythm),  two-measure  periods, 
four-measure  periods,  lastly  the  whole  or  eight-meas- 
ure period.  Just  as  each  shorter  period  is  balanced 
by  another  of  the  same  length,  just  so  the  larger  eight- 
measure  period  requires  another  eight-measure  period 
in  order  to  effect  a  balance.  Thus  the  repetition  of 
the  eight-measure  period  produces  a  still  greater  wave 
or  period  of  sixteen  measures.  The  possibilities  of 
rhythmic  expansion  are  alone  limited  by  the  percep- 
tive and  conceptive  faculties.  Although  our  example 
presents  the  simplest  form  of  rhythm  it  suffices  to 
illustrate  the  subrhythm  and  its  expansion.  On  the 
line  of  least  resistance  the  repetition  of  an  initial 
subrhythm  is  spontaneous;  however,  it  is  an  error  to 
speak  of  repetition  as  a  principle  of  form,  since  it  but 
superficially  describes  the  operation  of  the  actual  prin- 
ciple, equilibrium.  The  regular  alternations  and  repe- 
titions of  periods  long  and  short  are  plainly  due  to  the 
cardinal  shaping  principle,  equilibrium,  which  is  the 
vera  causa  of  balanced  motion  and  rhythmic  unity. 

Appearing  in  the  above  example  are  the  numbers 


ACCENT  AND  REGNANT  HARMONY         163 

2,  4,  8  and  16,  namely,  groups  of  two  beats,  and  of 
2,  4,  8  and  16  measures.  All  these  numbers  reappear 
in  the  potential  divisions  and  subdivisions  of  one  or 
both  of  the  subrhythmic  periods  or  beats  as  fol- 
lows :  — 


2 


r    r  i;   ;  I  :?   :5  II   ^  I  e^ 


Thus  we  observe  on  one  hand  the  expansion,  on 
the  other  the  division  and  subdivision  of  the  sub- 
rhythm,  the  latter  being  illustrative  of  what  I  have 
just  called  the  play  of  rhythm  upon  the  subrhythm. 
This  play  of  rhythmic  thought  upon  the  subrhythmic 
periods  is  further  illustrated  by  the  following  list  of 
rhythms  potential  in  a  single  period  of  the  subrhythm. 

1.  r 


y 


2. 

1/      or      -•    5      or      J    1 

3. 

e^     o.     q  ^     or     g^ 

4. 

f    fL^*      or      U    ^      or      ->    y 

5. 

UJ   <"  ^U   -  t^' 

6. 

LUS  or  q  IJI,'  or  '   q  r  f   • 

7. 

L/   o'  L=b' 

8. 

gj-     or      gj    q      or      q    f     or 

Students  after  working  out  this  list  resulting  from 
the  division  of  a  quarter-note  will  find  it  profitable 
to  work  out  other  lists  headed  by  notes  of  other 
denominations,  as  ^  ,  T  ,  J  .     Each  of  the  four  result- 


164  THE  NATURE  OF  MUSIC 

ing  lists  will  present  the  same  series  of  rhythms  and 
each  individual  rhythm  will  appear  in  another  set  of 
symbols  thus :  — 


1.  ° 

r 

r 

2.  r    r 

r     r 

r    r 

3.  r  r  r 

LJ  r 

f-r  ' 

etc.  etc.  etc.  etc. 

This  work  may  be  supplemented  by  four  other 
lists  in  which  the  unit  is  divided  into  three  parts  as 
follows :  — 

1.    ^-  f  f  f 

2.  r  r  r     r  r  r     lji^     £±/ 

3.  r  r  r  r     un     ^uj     ^'^  r 

etc  etc.  ete.  etc 

Such  rhythmic  work  will  cultivate  alertness  of  obser- 
vation and  is  stimulating  to  the  imagination.  How 
to  pursue  and  apply  such  work  will  readily  suggest 
itself  to  teacher  and  student. 

In  its  diversity  of  rhythmic  forms,  its  play  of 
rhythm  upon  rhythm,  its  inexhaustible  combina- 
tions, mixtures  and  groupings  of  the  most  diverse 
rhythms,  music  has  only  one  rival,  nature.  Although 
from  the  view-point  of  evolution  mensural  music  is 
but  a  thing  of  yesterday,  although  our  historians 
speak  of  much  of  the  ante-metrical  music  as  music 
without  rhythm,  nevertheless  when  we  consider  that 
all  motion  is  rhythm,  and  that  all  form  is  rhythmic 
form  shaped  by  equilibrium,  it  follows  that  rhythm- 


ACCENT  AND  REGNANT  HARMONY         165 

less  music  is  inconceivable  and  never  existed.  That 
it  never  did  exist,  and  that  tone  and  rhythm  have 
never  been  separated  in  music,  has  been  demon- 
strated and  proved  in  precedent  chapters  of  this 
book  by  the  truth  that  the  original  form  and  rela- 
tion of  tone,  namely,  consonance  and  dissonance  in 
one  voice,  had  their  genesis  in  the  stable  and  unstable 
equilibrating  periods  of  rhythm.  This  indissoluble 
union  of  rhythm  and  tone  took  place  not  by  any 
voluntary  effort  of  man,  but  under  the  impulse  of 
inherent  laws.  The  high  degree  of  rhythmic  com- 
plexity attained  in  primitive  music  is  a  familiar  fact 
of  history.  The  rhythm  of  primitive  chants  and  songs 
unaccompanied  by  instruments  was  emphasized  by 
words  or  gestures  or  both  together,  and  when  accom- 
panied by  instruments  the  rhythmic  emphasis  was 
further  intensified  by  drum,  pipe  and  string.  In  all 
this  musical  exercise,  the  results  of  which  must  have 
been  very  crude  in  its  early  stages,  common  feeling  of 
rhythmic  sound  was  its  common  guide,  while  pleasure 
in  and  love  of  rhythmic  sound  were  its  common 
stimuli.  Moreover,  this  exercise  in  its  early  stages 
was  marked  by  an  instinctive  and  unconscious 
obedience  to  inherent  and  unwritten  laws,  not  so 
difficult  to  be  sure  as  conscious  obedience  to  written 
laws.  The  effect  of  this  pleasure-gratifying  and  un- 
conscious law-abiding  exercise  of  the  music-sense  was 
the  slow  dawning  and  developing  of  that  keen  and 
accurate  perception  which  is  the  source  of  all  our 
knowledge  of  music,  the  evolution  of  perception 
being  the  road  upon  which  all  knowledge  has  been 
gained.      This  pleasure-gratifying  and   law-abiding 


166  THE  NATURE  OF  MUSIC 

exercise  in  rhythmic  sound  on  the  road  to  true  per- 
ception is  traceable  throughout  music's  development. 
The  story  of  the  development  of  pure  instrumental 
music  is  not  long  in  telling.  The  primitive  woods- 
man beat  upon  a  hollow  tree-trunk  and  the  sound 
pleased  him;  the  primitive  shepherd  blew  into  a 
reed  and  the  sound  pleased  him;  the  primitive  war- 
rior twanged  his  bowstring  and  the  sound  pleased 
him.  Because  the  sound  pleased  woodsman,  shep- 
herd and  warrior  they  kept  on  beating,  blowing  and 
twanging,  man  has  kept  on  beating,  blowing  and 
twanging  ever  since,  does  so  to-day,  and  promises  to  do 
so  in  the  future.  In  the  hollow  tree-trunk  the  prime- 
val woodsman  discovered  the  principle  of  the  drum, 
in  the  reed  the  shepherd  that  of  the  wind-instrument, 
in  the  bowstring  the  warrior  that  of  the  stringed  instru- 
ment. All  sorts  of  drums,  pipes  and  stringed  instru- 
ments in  all  sorts  of  shapes  were  fashioned  out  of  all 
sorts  of  materials  favoring  the  principle  of  each  class. 
Steadily  advancing  perception,  selection,  craft  and 
art  gradually  employed  and  combined  the  best  mate- 
rials, discovered  and  produced  new  materials,  modified 
and  improved  shapes,  added  new  principles  such  as 
stroke  of  bow  and  blow  of  hammer  on  string,  im- 
proved and  perfected  many  old  instruments,  discarded 
many  others  and  invented  new  ones.  And  all  this  was 
accomplished  under  the  impulse  of  steadily  evolving 
music-feeling  and  music-art  in  fulfilment  of  inherent 
laws  and  principles.  Result:  the  modern  orchestra 
with  its  choirs  of  perfected  instruments,  the  great 
organ,  the  pianoforte  and  their  respective  literatures. 
The  basic  group-numbers  of  rhythms  being  2  and  3, 


ACCENT  AND  REGNANT  HARMONY         167 

it  follows  that  the  forms  of  music-rhythms  are  as  diverse 
as  are  the  regular  and  irregular  combinations  of  these 
elementary  group-numbers,  first  in  the  subrhy  thm,  next 
in  the  potential  subdivisions  and  expansions  of  all  the 
potential  subrhythms,  which  is  to  say  that  the  diver- 
sity of  music-rhythms  is  limitless.  The  classification 
of  music-rhythms  is  roughly  outlined  under  the  four 
following  heads:  — 

I.    Simple  groups  of  2.     Simple  groups  of  3. 
II.    Compound  groups  of  2.     Compound  groups 
of  3. 

III.  Mixed  groups  of  2  and  3,  as  5,  7,  10,  11,  etc. 

IV.  Simultaneous  groups  of  2  and  3,  and  of  their 

compounds  and  mixtures. 
The  forms  of  I  and  II  are  regular;  those  of  III 
and  IV  irregular.  It  is  possible,  though  rare,  that  the 
subrhythmic  periods  and  all  the  shorter  and  longer 
periods  resulting  from  the  division  and  expansion  of 
the  subrhythm  may  be  regular  throughout.  But  what 
should  be  emphasized  here  is  the  fact  that  while  a 
subrhythm  may  be  regular  its  shorter  and  longer 
periods  may  present  many  irregular  forms,  and  con- 
versely, while  the  subrhythm  may  be  irregular  its 
shorter  and  longer  periods  may  present  many  regular 
forms.  This  great  variety  of  potential  subrhythmic 
forms,  the  limitless  possibilities  of  their  division  and 
expansion,  the  commingling  and  concurrence  of  regu- 
lar and  irregular  forms,  the  infinite  possibilities  in 
multi-voice  music  of  the  interplay  of  rhythms,  not 
only  of  one  rhythm  on  another  but  of  rhythms  upon 
rhythms,  all  this  plainly  intimates  the  inexhaustible 
wealth  of  music-rhythm. 


168  THE  NATURE  OF  MUSIC 

The  subrhythm,  the  written  form  of  which  is  the 
measure,  is  named  by  the  number  and  length  of  its 
periods,  therefore  by  its  measure  or  metre.  The  sub- 
rhythmic  period  is  a  beat  of  the  measure.  The 
measure  of  subrhythms  may  be  simple  dual  or  triple, 
compound  dual  or  triple,  mixed  dual  or  mixed  triple, 
that  is  to  say,  the  measure  may  contain  2  or  3  or  4  or  5 
or  6  or  7  beats.  The  measure  of  five  beats  is  mixed 
dual  because  5  is  divisible  into  two  parts,  namely, 

2  +  3  or  3  +  2.  The  measure  of  7  beats  is  mixed 
triple  because  7  is  divisible  into  three  parts,  namely, 

3  +  2  +  2,  2  +  3  +  2,  or  2  +  2+  3.  The  length 
of  a  subrhythmic  period  is  named  by  that  of  the  beat 
of  a  measure  and  may  be  a    I  or  J  or  ^  or  I^  ;  it  may 

also   be    a     1  ,      I  ,    JJn   or   j^.      Hence  the  various 

indices  of  the  measure  of  subrhythms  as  |,  |,  |,  |,  and 
so  on.  The  above  dotted  notes  are  suggested  as 
measure  units  and  may  be  marked  in  the  measure- 
index  by  a  corresponding  dot  after  the  number 
indicating  the  unit  as  1.  instead  of  %,  I  instead  of 
I,  I  instead  of  |,  |,  instead  of  |,  I,  instead  of  ^^,  etc. 
All  this  but  suggests  the  possibilities  of  diverse  sub- 
rhythmic  forms,  while  those  of  the  subdivisions  and 
expansions  of  those  subrhythms  must  needs  be  left 
to  the  suggestion  and  imagination  of  readers  and 
composers. 

Music  has  another  resource  for  variety  of  rhythms 
in  another  mode  of  division  peculiar  to  itself.  I  allude 
to  the  division  of  a  unit  into  three  parts  or  triplets  as 


a  .     .  3 


G>  into  p   p   p ,  p into  m   f   9y  m  into  #   ^   # ,  and  so 


ACCENT  AND  REGNANT  HARMONY 


169 


on.  There  are  yet  other  resources  arising  in  the 
play  of  the  imagination  upon  the  subrhythm;  for 
example,  the  play  of  a  3  on  a  subrhythmic  2,  of  a  5 
and  6  on  a  subrhythmic  4,  and  so  on,  not  to  mention 
the  possibilities  of  new  forms  arising  by  subdivision 
and  expansion  of  these  play-rhythms. 


a)  I  r  r 


1     I 


r  r 


Li'  r  r 


etc. 


b)t  r 


3 
f     F     P     ^ 

fill 


r  r  r  rr 


t^n^n^ 


Also  the  play  of  2,  4  and  5  on  a  subrhythmic  3, 
not  to  mention  possible  subdivisions  and  expansions, 
as  follows :  — 


ir 


r 


4 

r  r 


r 


r  r  r  r  r 


etc. 


Next,  an  example  (Chopin  Op.  42)  where  the 
melody  sings  a  2  to  the  subrhythmic  3,  the  former 
dividing  the  accompanying  figure  into  2x3,  the  latter 
dividing  it  into  3x2,  as  follows:  — 


hfhr    h_d 


r    r    r 


P     P 


r    r 


etc. 


Next,  an  example  (Schumann  "Des  Abends") 
where  the  melody  sings  3  to  the  subrhythmic  2  (a)) 
and  later  continues  the  same  thing  in  syncopation  as 
at  6). 


«)  2 

8 


£j/^f..^.^^d^.^ 


etc. 


170 


THE  NATURE  OF  MUSIC 


Our  next  example  illustrates  two  concurrent  melo- 
dies, the  subrhythm  of  one  of  which  is  I  or  1.,  while 
that  of  the  other  is  |. 


J          N    r-r-i 

J-^JJ  F. 

r      u 

N     1     H    1 
1       1                 1^ 

etc. 

W^f^fi'  ^ 

'^t          ^^» 

•  ^^        «   _ 

r      r 

r    f 

r-  f 

To  sum  up :   Below  are  the  five  forms  of  elementary 

periods. 

TWOS 

^         '^^—^      ^^ 

light     heavy         heavy    light 

THREES 

light     light     heavy 


light     heavy     light 


heavy     light     light 


Any  of  these  forms  may  be  the  subrhythmic  period 
of,  may  appear  in  the  smaller  and  larger  periods  of 
the  subrhythmic  divisions  and  expansions.  In  any 
period  the  above  forms  may  be  simple,  compound  or 
mixed.  In  simultaneous  rhythms  the  possible  concur- 
rences of  twos  and  threes,  their  compounds  and  mix- 
tures are  simply  endless.  A  single  larger  period  of 
simultaneous  rhythms  may  combine  the  greatest  vari- 
ety of  regular  and  irregular  forms.  No  single  music- 
work  is  so  rich  in  variety  of  rhythms  as  Bach's  "  Well- 
tempered  Clavichord."  Mozart  and  Beethoven,  the 
former  notably  in  the  subdivisions  of  the  subrhythm, 
the  latter  in  both  the  subdivision  and  expansion  of  the 


ACCENT  AND  REGNANT  HARMONY  171 

subrhythm,  present  a  great  diversity  of  forms.  More 
complex  rhythms  of  the  classes  III  and  IV  appear 
in  profusion  in  the  works  of  Berlioz,  Liszt  and 
Wagner,  of  Chopin,  Schumann  and  Brahms,  of 
Tschaikowsky,  Strauss  and  others.  Music's  struc- 
tural development  has  followed  the  natural  law  by 
which  forms  proceed  from  simple  to  complex,  from 
regular  to  irregular,  from  homogeneity  to  hetero- 
geneity. Music-rhythms  are  boundless  as  thought, 
imagination  and  expression;  they  are  however  the 
shapes  of  music-thought  itself  and  are  not  to  be 
viewed  and  treated  as  moulds  into  which  composers 
shape  music-thoughts  as  caterers  shape  cakes  and  ices. 
Music-thought  and  imagination  shape  tone-rhythm 
and  necessarily  obey  and  fulfil  the  law  of  being  inher- 
ent in  tone-rhythm.  Melody,  the  composite  of  the 
two  elements  rhythm  and  harmony,  the  flower  of 
music  and  the  essential  form  of  the  music-muse,  has 
undergone  great  structural  changes  and  will  undergo 
other  changes  as  the  evolving  music-muse  may  require. 
Greatly  as  old  and  modern  melodies  differ  in  structure 
yet  they  all  obey  and  fulfil  the  shaping  principle  of 
tone-rhythm  and  they  are  all  based  upon  a  common 
structural  unit,  namely,  the  phrase.  The  phrase 
appears  everywhere,  in  bird-song,  in  folk-song,  in 
the  melodies  of  all  composers.  Differences  in  struc- 
ture lie  first  of  all  in  the  form  and  next  in  the  treat- 
ment of  the  phrase.  The  phrase  as  presented  by 
self -developed  melody  in  a  state  of  nature  is  one  thing 
while  the  phrase  as  developed  in  the  creations  of 
music-art  is  quite  another  matter,  although  both  are 
links  in  a  chain  of  continuous  evolution.     In  fulfil- 


172  THE  NATURE  OF  MUSIC 

merit  of  the  shaping  principle  of  equilibrium  the  first 
great  end  and  aim  in  melody's  self-development  was 
perfect  symmetry,  and  this  meant  perfect  simplicity 
of  form.  In  a  state  of  nature  and  under  conditions 
of  complete  freedom  to  bud  and  blossom  into  perfect 
form  in  conformity  with  the  laws  of  its  being,  melody 
attained  this  end  and  aim  in  the  folk-dance  and 
folk-song  in  which  it  directly  and  spontaneously  voiced 
the  soul  of  the  people.  This  perfect  form  of  ideal 
beauty  attained  by  melody  in  a  state  of  nature  is 
nothing  short  of  wonderful.  In  melody's  structural 
development  its  two  elements  rhythm  and  harmony 
have  acted  and  reacted  upon  each  other  and  have 
played  an  equipollent  part.  The  simple  symmetrical 
melody  arose  under  the  predominating  influence  of 
rhythm  at  a  time  when  harmony  was  little  developed 
and  the  chord  unknown.  On  the  other  hand,  the 
more  complex  structures  of  modern  melodies  have 
arisen  under  the  predominating  influence  of  melody's 
rapidly  developing  element  of  harmony.  But  nothing 
could  be  wider  of  the  truth  than  the  view  that  in 
modern  music  melody  has  been  supplanted  and  super- 
seded by  harmony.  Melody  being  the  raison  d'etre 
of  harmony  could  not  be  supplanted  by  one  of  its 
elements.  I  repeat:  no  melody,  no  harmony;  no 
melody,  no  idea ;  no  melody,  no  music.  From  first  to 
last  music  is  melody  and  all  composers  are  melodists. 
In  fulfilment  of  the  shaping  principle  of  equili- 
brium short  and  simple  tone-rhythms  expanded  into 
symmetrical  phrases,  and  these  phrases  then  ex- 
panded into  the  symmetrical  folk-melody.  This  reg- 
ular expansion  of   the   subrhythm   into   larger   and 


ACCENT  AND  REGNANT  HARMONY         173 

larger  symmetrical  periods  lay  in  the  rhythmic  nature 
of  things.  Melody  in  a  state  of  nature  could  develop 
no  further  and  was  ripe  for  greater  things,  was  ready 
to  enter  the  realm  of  fine  art,  *'the  paradise  and  play- 
ground of  the  human  spirit."  Melody  did  enter  into 
this  domain  of  constructive  thought  and  imagination 
and  the  classic  form  of  music  took  root.  Regular 
symmetries  in  smaller  parts  and  wholes  naturally  led 
to  regular  symmetries  in  larger  parts  and  wholes. 
Hence  the  classic  sonata  and  symphony,  in  creating 
which  the  old  masters  simply  felt,  obeyed  and  fulfilled 
the  shaping  principles  of  tone-rhythmic  thought,  leav- 
ing it  to  others  to  define  these  principles.  Genius  was 
their  guide  and  law,  art  and  its  universal  message  was 
their  absorbing  end  and  aim.  Nothing  could  have 
been  more  natural  than  these  regular  symmetries  and 
the  prominence  of  the  group-numbers  2  and  4  both  in 
the  germinal  melodies  and  larger  structures.  Are 
not  nature's  most  obvious  rhythms  dual  and  regular, 
has  not  nature  produced  bipeds  and  quadrupeds  in 
fulfilment  of  equilibrium,  do  we  not  walk  on  two  feet 
and  group  our  steps  in  twos  and  fours .?  True  our 
modern  composers  have  profited  by  nature's  further 
teaching  that  there  are  countless  irregular  symmetries 
both  in  minute  forms  and  in  large  aggregates  and 
masses,  all  of  which  are  pervaded  and  ruled  by  har- 
mony. But  regular  symmetries  which  in  music  corre- 
spond w4th  perfect  simplicity  of  form  had  to  come  first 
and  did  come  through  the  influence  of  rhythm,  while 
through  the  influence  of  harmony  have  appeared  those 
irregular  symmetries  in  the  phrases,  melodies  and 
larger  structures  of  modern  music  which  have  been  so 


174  THE  NATURE  OF  MUSIC 

unjustly  condemned  as  unsymmetrical  because  they  do 
not  square  with  the  regular  symmetries  of  the  classic 
form.  However,  such  criticisms  as  well  as  the  concep- 
tion of  the  classic  forms  as  conventions  and  models  to 
be  strictly  adhered  to  have  their  origin  in  the  minds 
of  analyst  and  theorist,  who  necessarily  follow  "limp- 
ing" in  the  wake  of  genius.  In  a  previous  chapter 
a  distinction  was  drawn  between  rhythmic  time  and 
mathematical  time  or  clock-time:  the  former  has  the 
group-pulse  or  accent  which  the  latter  lacks.  The 
same  distinction  holds  between  rhythmic  and  mathe- 
matical symmetry.  The  regular  symmetries  of  the 
classic  form  are  rhythmic,  not  mathematical,  and 
therefore  the  classic  sonata  and  symphony  are  not 
to  be  likened  to  the  geometrical  patterns  of  French 
gardens  and  the  regular  squares  of  a  modern  city. 
Symmetry  in  music,  be  it  regular  or  irregular,  is  always 
rhythmic.  When  we  consider  that  rhythm  pervades 
body  and  soul  and  that  we  spontaneously  express  the 
group-pulse  or  accent  in  our  ordinary  bodily  move- 
ments and  speech,  it  is  strange,  to  say  the  least,  that 
so  large  a  proportion  of  performers  seem  not  to  know 
what  the  rhythmic  group-pulse  is  and  in  their  per- 
formances so  often  remind  us  of  clock-time. 

The  folk-melody  is  the  bloom  of  ages  upon  ages  of 
evolution,  and  its  perfect  form  of  ideal  beauty  is  one 
of  the  countless  wonders  of  nature.  The  thought 
and  imagination  which  developed  this  free-born 
melody  into  the  perfect  rhythmic  balance  and  unity 
of  the  classic  form,  and  which  is  so  simple  and  naive 
in  Haydn,  so  pure  and  balanced  in  Mozart,  so  great 
and  potent  in  Bach  and  Beethoven,  constitute  the 


ACCENT  AND  REGNANT  HARMONY         175 

record  of  music's  first  great  wave  of  development  as 
an  art.  The  classic  form  is  not  only  to  be  regarded 
as  the  necessary  culmination  of  a  wave  of  psychical 
development,  but  is  an  ideal  and  spiritual  achievement, 
an  eternal  glory,  which  no  extravagance  of  language 
can  overestimate.  In  it,  all  that  has  followed  is 
rooted,  for  music-art  is  a  continuous  evolution,  the  old 
and  the  new  being  one  in  kind  and  links  of  one  chain. 
In  music,  as  in  all  the  arts,  the  classic  constitutes  the 
firm  rock  of  its  school,  it  is  the  basic  school  of  music- 
culture  for  composers,  performers  and  listeners. 
Composers  and  performers  thus  schooled  are  quickly 
detected.  "Learning  to  know  the  best  that  has  been 
thought,  said  and  done,"  this,  Matthew  Arnold  tells 
us,  is  culture.  For  music-culture  we  should  therefore 
turn  first  of  all  to  the  old  masters  whose  works 
clearly  reveal  the  fundamental  principles  of  tone-art. 
We  may  then  turn  to  the  modern  masters  not  for  the 
purpose  of  learning  as  some  think  how  they  have 
violated  laws,  but  to  continue  our  culture.  Genius 
enforces,  does  not  violate,  laws.  Its  ideal  and  spiritual 
content,  the  potency  and  universality  of  its  message, 
not  its  specific  form,  constitute  its  justification  and 
greatness  before  the  tribunal  of  beauty,  the  art-deity. 
This  message  and  greatness  like  beauty  itself  are 
mysteries,  yet  in  the  presence  of  a  great  work  of  art 
they  are  realities:  the  beauty  of  the  work  is  unmis- 
takable, es  packt 


CHAPTER   V 

ORIGIN  AND  NATURE  OF  MINOR 

43.    Origin  of  the  Minor  Consonance 

With  the  subject  before  us  we  resume  our  study  of 
the  evolution  of  harmony  in  one  voice,  which  is  the 
self-asserting  harmony  of  melody.  Music  began  with 
one  voice,  that  is,  with  melody,  wherefore  origins  are 
to  be  sought  in  one  voice  or  melody.  Our  study  is 
centred  in  melody,  our  facts  are  the  common  har- 
monic reports  of  melody,  our  test  of  truth  is  common 
feeling  and  perception  of  the  self-reports  of  melody. 
This  confirmed  by  common  experience  and  observa- 
tion is  the  truth  of  our  theses,  namely,  that  melody  is 
the  indissoluble  composite  of  rhythm  and  harmony 
and  not  an  element;  that  melody  apart  from  mode, 
that  mode  apart  from  harmony  do  not  and  never  did 
exist;  that  in  one  voice  the  harmonic  reports  of 
melody  are  common  reports  and  are  not  mutable 
except  through  arbitrary  personal  selection;  that  the 
efiicient  accent  on  an  isolated  tone  always  generates 
the  major  consonance,  in  other  words,  that  the 
natural  harmony  of  a  tone  is  major.  Independently 
the  last  thesis  suffices  to  establish  the  priority  of  the 
major  consonance  and  mode.  But  overwhelming 
and  conclusive  evidence  of  the  priority  of  major  is 
furnished  by  bird-songs  and  primitive  melodies  most 
of  which  are  in  major  while  the  proportion  of  those 


ORIGIN  AND  NATURE  OF  MINOR  177 

in  minor  is  exceedingly  small.  The  major  mode  arose 
when  the  major  consonance  arose;  the  minor  mode 
arose  when  the  minor  consonance  arose:  the  ques- 
tion of  the  origin  of  the  mode  therefore  resolves 
itself  into  that  of  the  origin  of  the  consonance  with 
which  it  sprang  into  being  and  in  which  it  is  rooted. 
How  melody  brought  forth  major  has  been  fully 
explained.  How  melody  brought  forth  minor  is  the 
study  confronting  us. 

An  isolated  tone  never  generates  and  reports  the 
minor  consonance.  It  is  true  that  on  an  isolated 
tone  we  may  think  and  hear  the  minor  chord  as  we 
may  any  one  of  a  hundred  other  chords,  but  in  so 
doing  we  think  and  hear  what  we  select,  not  what  a 
tone  itself  asserts  and  reports.  Now  in  this  our  study 
of  one  voice  or  melody  everything  hinges  upon  our 
power  to  discriminate  between  the  self-report  of  a 
tone  and  personal  selection.  The  former  alone  is 
free  from  bias  and  has  value ;  the  latter  is  all  bias  and 
valueless.  Whether  discrimination  between  the  two 
be  easy  or  difficult,  in  no  way  affects  the  truth  of  our 
thesis  that  an  isolated  tone  never  reports  the  minor 
consonance,  nor  does  it  affect  any  of  our  data  and 
theses. 

In  evolution  a  new  something  springs  from  a  previ- 
ously existing  something.  Since  major  came  before 
minor  it  follows  that  minor  sprang  from  elements 
previously  existing  in  major.  We  have  explained 
how  melody  began  by  intoning  the  rhythmic  relation 
of  cadence  and  repose  and  thus  brought  forth  the 
major  consonance  and  its  cadences,  that  is,  the  major 
mode.     Hence  our  thesis:  the  form  of  harmony  is 


178  THE  NATURE  OF  MUSIC 

due  to  relation.  Later  we  demonstrated  that  certain 
changes  in  relation  generate  new  forms  of  harmony. 
Hence  our  thesis :  new  forms  of  harmony  spring  from 
previously  existing  tones  in  new  or  transmuted  rela- 
tions. This  thesis  points  out  the  solution  of  the 
centuries-old  puzzle  as  to  the  origin  and  nature  of  the 
minor  consonance  and  mode.  It  required  at  least 
two  tones  and  a  specific  relation  potential  in  those  two 
tones  to  generate  the  minor  consonance  in  feeling  and 
perception.  The  two  tones  in  which  that  specific 
relation  was  potential  previously  existed  in  major. 
What  are  the  two  tones,  what  the  specific  relation.? 
The  tones  are  do  and  la,  the  relation  is  a  small  third. 
The  downward  step  do  to  la  with  the  efficient  accent 
on  la  generates  the  harmonic  thread  of  the  minor 
consonance  as  follows:  — 


i 


^^^3 


I 


¥ 


^^ 


do    la       do    la         / 


This  I  claim  to  be  the  origin  of  the  minor  conso- 
nance and  mode  in  one  voice.  Our  example  illustrates 
the  self-assertion  of  the  minor  consonance  and  demon- 
strates that  this  specific  form  of  harmony  springs 
from  the  repose  or  stable  equilibrium  inherent  in  the 
specific  relation  of  the  small  third  formed  by  do  and 
la.  Apart  from  two  tones  in  the  above  relation  of 
a  small  third  the  minor  consonance  cannot  be  felt, 
heard,  thought  or  expressed,  and  therefore  could  not 
have  been  generated  and  asserted  by  melody.  On 
the  other  hand,  apart  from  this  consonance  which  we 


ORIGIN  AND  NATURE  OF  MINOR  179 

all  recognize  and  therefore  relate  as  the  minor  Tonic- 
harmony  it  is  impossible  to  feel,  perceive  or  conceive 
the  minor  mode. 

In  one  voice,  specific  relations  of  specific  tones  give 
rise  to  and  report  specific  forms  of  stable  and  unstable 
harmonies,  that  is,  of  consonances  and  dissonances. 
Just  what  these  specific  relations,  tones  and  forms  of 
harmony  are  we  learn  from  our  common  feeling  and 
perception  of  the  self-reports  of  melody.  In  observ- 
ing and  verifying  the  common  reports  in  one  voice  we 
stand  on  common  intellectual  ground,  for  when  that 
which  we  think,  fully  and  faithfully  interprets  the 
common  feeling  and  percept  then  only  shall  we  agree 
as  to  the  facts  or  common  reports.  I  repeat:  our 
concepts  in  one  voice  are  false  when  they  conflict, 
and  true  when  they  completely  accord  with  our 
common  feeling  and  percept,  that  is,  with  the  common 
report  of  melody.  Now  the  small  third  is  the  only 
relation  that  gives  rise  to  and  reports  the  minor 
consonance.  I  next  present  three  theses  based  upon 
common  reports. 

1.  Any  isolated  combination  of  two  tones  in  the 
relation  of  a  small  third  generates  and  reports  the 
minor  consonance  which  we  all  involuntarily  recog- 
nize and  relate  as  the  minor  Tonic-harmony. 

2.  An  isolated  major  consonance  invariably  reports 
its  root  to  be  do,  its  third  to  be  mi,  its  fifth  to  be  soL 

3.  An  isolated  minor  consonance  invariably  reports 
its  root  to  be  la,  its  third  to  be  do,  its  fifth  to  be  mi. 

The  three  components  of  the  major  consonance  are 
major  harmonic  percepts  which  I  mark  with  larger 
numbers.     The  three  components  of  the  minor  con- 


180  THE  NATURE  OF  MUSIC 

sonance  are  minor  harmonic  'percepts  which  I  indicate 
by  smaller  numbers.  Both  consonances  and  their 
symbols  are  given  below  for  comparison  and  correla- 
tion. 

1     3      5 

1.  Major  Tonic-harmony :     do  —  mi  —  sol 

18  6 

2.  Minor  Tonic-harmony :    la  —  do  —  mi 


Upon  the  priority  of  major  we  base  our  thesis  that 
minor  has  been  derived  from  elements  previously 
existing  in  major.  Thus  major  supplied  the  original 
tones  named  diatonics  which  in  minor  reappear  in 
new  and  transmuted  relations.  Note  do  and  la  in 
the  above  example.  Do,  the  major  Tonic  and  the 
original  root  (1),  of  the  genus  consonance,  reappears 
in  minor  as  small  third  (3)  of  the  minor  consonance. 
La,  the  original  ninth  (9)  of  the  genus  dissonance,  in 
which  it  is  the  highest  tone,  reappears  in  minor  as 
the  original  minor  Tonic  and  root  (1)  of  the  original 
minor  consonance.  Thus  again,  major  supplied  the 
original  forms  of  consonance  and  dissonance,  each  of 
which  assumes  a  new  and  transmuted  form  in  minor. 
Our  example  presents  the  original  and  transmuted 
forms  of  consonance.  Thus  again,  major  supplied  the 
basic  relations  of  rising  cadence,  falling  cadence  and 
repose  which  characterize  and  underlie  tone-relation 
in  general  and  mode-relation  in  particular  and  which 
in  minor  are  directly  imitated.  Minor  is  therefore 
not  only  derived  but  is  purely  imitative;  it  is  derived 
from  material  provided  by  the  prototype  major,  and 
it  imitates  the  relations  of  cadence  and  repose  ori- 


ORIGIN  AND  NATURE  OF  MINOR  181 

ginally  derived  from  rhythm  and  first  intoned  by 
melody  in  the  prototype  major  mode.  Here  we  note 
in  passing  that  imitation  is  not  alone  a  principle  of 
music-structure  as  demonstrated  in  round-song,  anti- 
phonal  chant,  sequence,  canon  and  fugue,  but,  what 
is  even  more  important,  imitation  is  a  principle  of 
harmonic  genesis  closely  allied  to  that  of  potential 
harmony,  the  subject  of  a  later  chapter.  Again  re- 
ferring to  our  example  we  note  that  do  is  the  origi- 
nal major  Tonic,  that  c^o-major  is  the  original  major 
mode;  next,  that  la  is  the  original  minor  Tonic,  that 
Za-minor  is  the  original  minor  mode  and  corresponds 
with  what  is  known  as  relative  minor.  The  almost 
universal  adoption  of  relative  minor  as  the  true  minor 
amounts  to  a  tacit  acknowledgment  of  the  priority 
of  major,  and  presents  but  one  of  thousands  of  cases 
in  which  our  great  thinkers  draw  their  conclusions 
from  facts  reported  by  common  feeling  and  perception. 
In  all  books  on  music,  be  they  historic,  biographical, 
aesthetic,  theoretic  or  didactic,  we  everywhere  find 
the  direct  appeal  to  music-feeling  for  every  hidden 
and  ultimate  truth.  It  is  safe  to  say  that  every  truth 
that  came  to  stay  in  the  books  came  by  way  and 
sanction  of  music-feeling.  The  conflict  between  an 
abstract  theory  and  concrete  feeling  waxes  strong  in 
every  case  where  the  two  are  irreconcilable  owing  to 
the  unconquerable  protest  and  revolt  of  music-feeling. 
One  of  a  number  of  cases  in  point  is  the  Zarlino- 
Riemann  theory  of  pendant  minor  with  harmonic 
roots  in  air  upon  which  we  will  later  on  present  the 
common  harmonic  self-reports  of  one  voice  or  melody. 
The  concept  of  minor  as  la  minor  (relative  minor) 


182  THE  NATURE  OF  MUSIC 

completely  harmonizes  with  our  common  feeling  and 
percept  of  minor,  and  its  validity  is  demonstrated  and 
confirmed  by  the  self-reports  of  melody. 

Reverting  to  our  theses  on  page  179  it  may  be  asked, 
why  fix  upon  the  specific  tones  do  and  la  for  the  origin 
of  minor?  Among  previously  extant  diatonics  are 
there  no  other  combinations  of  two  tones  in  which  the 
requisite  relation  of  a  small  third  is  potential  ?  Ages 
upon  ages  before  there  was  any  conscious  perception 
of  harmony,  melody  had  brought  forth  both  the  major 
mode  and  minor  mode  in  one  voice.  In  connection 
with  this  early  formative  period  of  melody  when  feel- 
ing of  harmony  was  in  its  incipient  stages  of  develop- 
ment we  could  not  confidently  speak  of  specific  tones 
or  of  specific  relations  generating  specific  forms  of  har- 
mony, in  short,  we  could  not  answer  the  above  ques- 
tions, were  it  not  for  harmony  in  one  voice,  its  definite 
self-reports  and  its  demonstrable  principles.  Admit- 
tedly the  refined  harmonic  sense  of  to-day  is  connected 
with,  rooted  in,  and  the  evolutionary  product  of,  the 
harmonic  sense  of  the  entire  past,  or  briefly,  of  yester- 
day, and  it  follows  that  the  harmonic  percepts  of 
to-day  spring  from  the  harmonic  feelings  of  yesterday, 
that  the  common  self -reports  of  melody  so  clearly  per- 
ceived to-day  are  the  same  which  yesterday  were  but 
dimly  felt.  Thus  harmony  in  one  voice  is  the  connect- 
ing link  between  the  harmony  of  the  present  and  that 
of  the  entire  past,  and  by  means  of  its  self-reports  we 
can  trace  the  genesis  of  tone  upon  tone,  relation  upon 
relation,  harmonic  form  upon  harmonic  form;  and 
because  these  self-reports  are  common  and  apply  to  all 
music  in  one  voice  it  matters  little  whether  our  illustra- 


ORIGIN  AND  NATURE  OF  MINOR  183 

tions  are  drawn  from  modern  or  primitive  melodies,  or 
whether  we  devise  them  as  we  proceed,  so  long  as  they 
are  in  one  voice  and  exemplify  the  special  case  under 
consideration.  We  may  now  answer  the  above  ques- 
tions beginning  with  the  second.  Yes,  there  are  three 
other  combinations  of  diatonics  which  frequently  ap- 
pear in  primitive  melodies  in  the  relation  of  small 
thirds.  One  is  sol  down  to  mi,  which  like  do  to  la 
dates  back  as  far  as  the  pentatonic  period,  and  which 
insistently  reports  the  major  Tonic-harmony  (I),  sol 
asserting  itself  as  5,  mi  as  3.  Later  on  when  the  down- 
leader /a  and  the  upleader  ti  had  made  their  appear- 
ance, melody  introduced  two  other  combinations, 
namely, /a  down  to  re,  re  down  to  ti.  During  the  ante- 
minor  stage  of  music  when  melody  had  evolved  but  a 
scant  web  of  harmonic  threads  and  had  generated  at 
most  three  regnant  harmonies,  namely,  I,  V  and  IV, 
not  one  of  these  combinations  in  small  thirds  could 
have  generated  the  minor  consonance.  Why  not? 
Simply  and  obviously  because  these  original  har- 
monies of  melody  necessarily  and  always  appear  in 
correlation,  as  demonstrated  by  primitive  melodies  of 
birds  and  men.  Because  of  this  necessary  correlation 
the  combinations /a  to  re  and  re  to  ti  insistently  report 
the  major  Dominant-harmony  (V),/a  asserting  itself 
as  7,  r^  as  5,  ti  as  3.  Indeed,  the  original  relations  of 
original  tones  are  so  deeply  rooted  in  harmonic  feeling 
that  even  to-day  we  cannot  change  them  except 
through  deliberate  reflection  and  a  voluntary  effort  of 
selection  which  in  every  such  case  results  in  a  modula- 
tion. Needless  to  say  it  would  be  the  height  of  ab- 
surdity to  accuse  man  of  such  refined  intellectual 


184  THE  NATURE  OF  MUSIC 

powers  of  abstraction  at  a  time  when  his  melodies  were 
the  simple,  naive  and  spontaneous  intonations  of  con- 
crete feelings.  Of  these  primitive  melodies  and  of  the 
beautiful  folk-melodies  and  of  the  immortal  melodies 
of  our  masters  two  things  are  equally  true:  not  one 
was  ever  produced  through  deliberate  reflection,  and 
no  one  can  t6ll  whence  they  came.  Of  all  the  seven 
diatonics  do  and  la  are  the  only  two  tones  through 
which  melody  could  have  brought  forth  the  minor  con- 
sonance, and  this  paragraph  may  be  concluded  by 
restating  our  thesis. 

Any  isolated  combination  of  two  tones  in  the  rela- 
tion of  a  small  third  generates  in  feeling  the  minor  con- 
sonance, and  in  every  such  case  the  two  specific  tones 
are  do  and  la. 

44.    Original  and  Duplicate  Forms  of  Harmony 

Each  specific  form  of  harmony  in  one  voice  arose  on 
a  specific  tone  in  a  specific  relation:  every  such  form 
being  the  first  of  its  kind  is  classed  as  the  original,  and 
every  repetition  of  such  an  original  on  other  tones  is 
classed  as  a  duplicate. 

In  the  whole  realm  of  harmony  there  are  but  two 
forms  of  consonances,  the  major  form  with  its  distinc- 
tive and  characteristic  large  third  (3),  the  minor  form 
with  its  distinctive  and  characteristic  small  third  (a). 
Of  the  two  consonances  the  major  form  is  the  proto- 
type, the  minor  form  is  the  derived  and  modified  type. 
Their  distinctive  thirds  at  once  mark  the  structural 
difference  between  the  two  forms  and  the  individual- 
ity and  essential  character  of  each.  The  major  Tonic- 
harmony  based  on  do  is  the  original  major  form:  the 


ORIGIN  AND  NATURE  OF  MINOR  185 

minor  Tonic-harmony  based  on  la  is  the  original 
minor  form.  In  evolution  these  forms  are  repeated 
on  other  tones,  and  all  such  repetitions  for  lack  of  a 
better  name  are  here  called  duplicates.  Duplicates 
of  the  major  form  on  V  and  IV  have  already  been  pre- 
sented and  explained  and  others  will  follow.  Dupli- 
cates of  the  minor  form  will  appear  presently. 

Roman  numbers  are  employed  for  the  double  pur- 
pose of  indicating  the  root  and  the  specific  form  of  a 
harmony;  in  larger  type  they  indicate  major,  in 
smaller  type,  minor  harmonies.  I  shall  strictly  adhere 
to  this  universal  custom  save  in  one  particular,  namely, 
the  numbers  indicating  minor  harmonies  will  be 
printed  in  italics  for  reasons  which  will  become  obvious 
as  we  proceed. 

45.  Origin  in  One  Voice  of  the  Minor  Form  of 
Dissonance.  Original  Cadences  of  the  Minor 
Mode 

In  minor  the  diatonics  owing  to  their  reappearance 
in  new  and  transmuted  relations  undergo  a  redistribu- 
tion and  regrouping.  The  prototype  modal  relations 
of  cadence  and  repose  in  precedent  major  are  directly 
imitated  in  minor,  and  these  imitative  relations  consti- 
tute the  vera  causa  of  the  genesis  of  the  minor  forms  of 
consonance  and  dissonance  which  are  the  counterparts 
in  minor  of  the  two  major  prototypes.  For  the  group 
of  tones  and  relations  which  we  have  named  the  reg- 
nant major  Tonic  and  its  cadences  there  is  a  corre- 
sponding minor  group,  the  regnant  minor  Tonic  and 
its  cadences ;  for  each  specific  tone  and  relation  in  the 
precedent  major  group  there  is  a  corresponding  tone 


186 


THE  NATURE  OF  MUSIC 


and  relation  in  the  derived  and  imitative  minor  group. 
In  short,  everything  in  major  has  its  parallel  and 
counterpart  in  minor.  Major  provided  the  material 
by  means  of  which  melody  produced  minor,  and  minor 
in  its  turn  has  added  new  material.  Just  as  in  major 
so  in  minor,  the  cadence-tones  arose  over  and  under 
and  tend  up  and  down  into  the  regnant  Tonic-har- 
mony. Because  of  these  corresponding  tones,  relations 
and  harmonies  in  the  two  modes,  parallel  examples 
in  major  and  minor  will  be  given  in  all  cases  where 
they  will  add  to  the  clearness  of  our  exposition.  Our 
first  example  presents  a  pentatonic  melody,  in  which 
note  the  common  harmonic  self -reports  and  corre- 
sponding tones,  relations  and  harmonies  in  the  two 
modes.  The  pitch  of  these  and  other  examples  is 
chosen  for  convenience  of  presentation  and  should  be 
thought  an  octave  lower. 


Major 


i 


g 


sol 


mi 

I- 


do        mi 


sol 


^ 


la 


sol 


I 


Minor 


i 


m 


e^ 


mt 


do 
I 


la 


do 


fa 


n 


Carefully  compare  these  parallel  examples.  The 
syllables  and  harmonic  numbers  show  the  new  and 
transmuted  relations  of  the  diatonics  in  minor.  Ob- 
serve that  each  mode  is  represented  by  the  three  com- 


ORIGIN  AND  NATURE  OF  MINOR  187 

ponents  of  the  Tonic-harmony,  by  one  component  of 
its  Dominant,  by  one  component  of  its  Subdominant. 
Observe  the  parallel  regnant  harmonies,  /  in  minor, 
the  counterpart  of  I  in  major.  Tone  upon  tone  com- 
pare the  corresponding  tones  and  harmonic  percepts  of 
the  two  modes  as  follows :  mi  s  in  minor  is  the  counter- 
part of  sol  5  in  major,  do  a  of  mi  3,  ti  5  of  re  5,  la  i  of 
do  1,  and  so  on.  The  essentially  imitative  character 
and  nature  of  the  minor  mode  is  plainly  manifest  not 
only  in  the  whole  meloharmonic  phrase,  but  in  each 
tone  and  interval,  each  progression  and  cadence,  each 
harmonic  percept.  Observe  the  parallel  falling  ca- 
dences :  ti  5  to  la  1  in  minor  corresponds  with  re  5  to 
do  1  in  major, /a  s  to  mis  in  minor  with  la  3  to  sol  5  in 
major.  Observe  that  the  cadence-tone  ti  5  in  minor 
reports  its  concomitant  third  to  be  a  large  third  and  a 
chromatic,  namely,  si  (gjlj!  in  our  example),  and  that 
this  chromatic  is  the  minor  upleader  which  corre- 
sponds with  the  major  upleader  ti  3.  Observe  in  the 
falling  cadence/a  to  mi  (f  to  e)  in  minor  how  unnatural 
it  would  be  to  substitute  fjjl  for  f.  These  observations 
will  have  an  important  bearing  on  the  sequel. 

The  major  Dominant  (V)  was  first  announced  and 
represented  in  melody  by  its  fifth  re  and  first  appeared 
in  cadence,  that  is,  as  a  byharmony.  The  same  is 
true  (see  above  example)  of  the  corresponding  minor 
Dominant  (V)  which  was  first  announced  and  repre- 
sented by  its  fifth  ti  (counterpart  in  minor  of  the  major 
re)  and  likewise  first  appeared  in  cadence  as  a  by- 
harmony.  Again,  the  major  Subdominant  (IV)  was 
first  reported  by  its  third  la,  the  parallel  minor  Sub- 
dominant  (as  in  example)  by  its  third /a.     Thus  the 


188 


THE  NATURE  OF  MUSIC 


part  played  by  re  and  la  in  major  is  repeated  in  minor 
by  its  corresponding  tones  ti  and  fa.  Thus,  as  we 
have  seen,  the  efficient  accent  on  re  generated  the  reg- 
nant Dominant  (V)  in  major;  hkewise  the  efficient 
accent  on  ti  generated  the  regnant  Dominant  (F)  in 
minor.  Again,  the  efficient  accent  on  la  caused  the 
genesis  of  the  regnant  Subdominant  (IV)  in  major,  on 
fa  the  corresponding  regnant  Subdominant  {iv)  in 
minor.  In  the  parallel  examples  below  compare 
these  corresponding  regnant  harmonies  and  note  the 
harmonic  reports  upon  their  genesis  as  just  ex- 
plained. 


Major 


m 


g 


I 


IV 


Minor 


m 


^i 


IV 


Our  next  consideration  is  the  minor  form  of  dis- 
sonance and  how  it  arose.  The  entire  harmonic 
thread  (comprising  five  components)  of  the  genus  dis- 
sonance (prototype  major  form)  was  and  is  latent  in 
the  major  cadence-tone  re.  Likewise  the  entire  har- 
monic thread  (comprising  five  components)  of  the 
derived  and  transmuted  form  of  dissonance  in  minor 
was  and  is  latent  in  the  corresponding  minor  cadence- 
tone  ti.  Compare  the  two  in  the  following  example :  — 


Major 


ORIGIN  AND  NATURE  OF  MINOR  189 

5       3135^53135,  9^5    31 


:^=¥ 


H — i — m — I — H 


T'  I  i-f  m 


re 


V  V^  V9 

5        3136,53135,  »,    531 


Minor 


^ 


^%^f^^ttf-^=^t^ 


r  V,  n 

The  two  forms  are  again  presented  in  syllables  and 
harmonic  numbers  for  further  observations. 

13     5      7      9 

1.  Major  V9 :  sol  —  ti  —  re  —  fa  —  la 

1  O  O  7  o 

2.  Minor  VqI  mi  —  si  —  ti  —  re  —  fa 

Compare  corresponding  tones  and  harmonic  per- 
cepts as  follows:  sol  is  root  of  major  Dominant,  mi 
is  root  of  minor  Dominant,  and  so  on.  Observe  that 
the  two  dissonances  differ  only  in  their  ninths,  all  the 
other  intervals  being  the  same;  the  ninth  in  major  is 
large  and  was  first  reported  by  /a,  the  ninth  in  minor 
is  small  and  was  first  reported  by /a.  The  distinctive 
individuality  of  each  of  the  two  types  of  consonances 
is  due  to  its  characteristic  third,  3  in  major,  s  in  minor, 
while  that  of  each  of  the  two  original  types  of  disso- 
nances is  due  to  its  characteristic  ninth,  9  in  major, 
9  in  minor.  Both  types  of  dissonances  confirm  the 
truth  of  our  thesis  that  the  ninth  is  the  highest  har- 
monic component  of  a  harmonic  root  and  therefore  the 
genetic  limit  of  harmony. 


190 


THE  NATURE  OF  MUSIC 


Sol  is  the  bond-tone  connecting  the  cadence  and 
repose  groups  of  harmony  V9 — I  in  major,  appearing 
first  as  5  of  I,  thereafter  as  1  of  V.  Likewise  mi  is 
the  bond-tone  of  the  corresponding  groups  of  har- 
monies Fg — I  in  minor  and  Hkewise  mi  appeared  as 
6  of  z  before  appearing  as  1  of  F.  Both  bond-tones 
are  next  presented. 


Major 


$ 


I- 


-<5>- 


V- 


I 


Minor 


i 


w= 


13       5 


f 


^^ 


Just  as  the  major  dissonance  arose  in  relation  to  the 
major  consonance  just  so  the  minor  dissonance  arose 
in  relation  to  the  minor  consonance.  The  remaining 
four  components  of  the  two  dissonances  are  cadence- 
tones  which  lie  directly  over  and  under,  and  which 
tend  and  resolve  up  and  down  into  the  components 
or  repose-tones  of  the  two  consonances.  Of  the  four 
in  major  all  are  diatonics  and  had  their  genesis  in 
relation  to  the  major  consonance.  Of  the  four  in 
minor  three  are  previously  existing  diatonics  in  trans- 
muted relations  while  one  {si,  the  chromatic)  is  a 
newly  derived  tone  the  genesis  of  which  we  have  just 
explained.     The  four  in  minor  directly  imitate  the 


ORIGIN  AND  NATURE  OF  MINOR 


191 


four  in  major.     Compare  below  the  four  cadence- 
tones  and  three  repose-tones  in  each  of  the  two  modes. 


Major 


Cadence-Tones 

3         5 


i 


^ 


9 


Repose-Tones 

1         3 


I 


Minor 


$ 


3       6 


kt 


^ 


I 


In  this  relation  the  four  cadence-tones  present  an 
aggregate  of  five  cadences  in  each  mode  since  ti  in 
minor  resolves  both  up  and  down  like  its  prototype 
re  in  major.  Each  cadence  in  minor  imitates  and 
is  the  counterpart  of  its  corresponding  cadence  in 
major.     Compare  the  five  parallel  cadences  below. 


3      15      15      3 

1.     Major:  ti       do         re       do         re       mi 


fa       mi 


9     5 

la     sol 


3       ^ 
2.     Minor:  si       la 


5     X 

ti       la 


"  8 

ti       do 


7  3 

re       do 


e        5 

fa       mi 


The  resolutions  of  these  cadences  are  next  presented 
in  the  form  of  chords  as  follows:  — 

Major  Minor 

\ 


V9     I 


192  THE  NATURE  OF  MUSIC 

The  addition  of  a  terminal  Tonic  to  each  of  the 
above  groups  of  four  cadence-tones  and  three  repose- 
tones  completes  the  scales  known  as  diatonic  major 
and  relative  minor.  They  are  presented  below  both 
ascending  and  descending  for  the  purpose  of  exhibiting 
their  parallel  progressions  and  resolutions  or  cadences, 
the  latter  marked  by  slurs. 


Major 


Minor 


I 


9=fS 


m-^ 


-^L 


do 


^-  ^^     "  '    ^    TTl^ 


la 

In  all  the  preceding  illustrations  of  parallel  cadences 
we  note  how  each  cadence  in  minor  has  arisen  by 
imitating  its  major  prototype.  Thus  the  upleader 
si  3  in  minor  corresponds  with  the  upleader  ti  3  in 
major,  the  downleader  re  ?  in  minor  with  the  down- 
leader  fa  7  in  major,  the  double  cadence  of  ti  5  with 
that  of  its  prototype  re  5,  the  cadence  of /a  q  with  that 
of  its  prototype  la  9.  In  short,  each  tone  and  relation 
in  major  is  offset  by  a  corresponding  tone  and  rela- 
tion in  minor.  Hence  the  close  relationship  of  major 
and  minor.  Each  mode  has  its  own  specific  form  of 
consonance  and  specific  form  of  dissonance  at  its 
foundation,  and  let  us  remember  that  in  one  voice, 
melody  generated  all  these  forms  in  obedience  to  the 
inherent  and  uniform  laws  of  causation  which  we 
have  already  defined. 

The  above  minor  group  of  tones  is  as  noteworthy 
for  the  absence  of  sol,  the  only  diatonic  which  does 


ORIGIN  AND  NATURE  OF  MINOR  193 

not  appear,  as  it  is  for  the  presence  of  the  newly 
generated  tone  si.  As  regards  si,  which  arose  as  a 
concomitant  in  the  harmonic  thread  generated  hjti5, 
we  pause  here  to  observe  first,  that  chromatics  first 
arose  as  concomitants  and  were  generated  by  diatonics 
in  transmuted  or  new  relations;  next,  that  all  newly 
generated  tones  like  si  pass  through  three  consecu- 
tive stages  of  psychological  evolution  which  mark  the 
progressive  development  of  melody.  Indeed,  with 
the  exception  of  the  components  of  one  harmony,  all 
tones  have  passed  through  these  three  evolutionary 
stages.  The  one  exception  is  the  major  Tonic-har- 
mony which  was  at  once  a  regnant  harmony  and  the 
first  harmony  generated  by  melody  and  whose  com- 
ponents do  1,  mi  3,  sol  5  therefore  made  their  first 
appearance  in  melody  as  regnant  tones.  The  three 
consecutive  psychological  stages  are  as  follows:  — 

First  Stage :  in  which  a  tone  had  its  genesis  as  an 
elementary  harmonic  or  concomitant  in  a  thread  of 
harmony  generated  by  a  previously  existing  tone  in  a 
new  relation.  This  is  a  tone's  lowest  or  elementary 
stage. 

Second  Stage :  in  which  a  tone  has  been  differen- 
tiated and  has  appeared  in  melody  as  a  bytone,  that 
is,  in  the  relation  of  cadence  on  a  light  rhythm-period. 
In  this  stage  a  tone  has  become  an  individual  con- 
stituent of  melody  and  of  the  tone-system.  This 
stage  may  be  called  briefly  the  bytone  stage. 

Third  Stage :  in  which  a  tone  has  appeared  in 
melody  as  a  regnant  tone.  In  this  stage  a  tone  first 
appears  on  light  rhythm-periods  after  or  between 
other  co-harmonics  of  the  regnant  harmony,  but  does 


194 


THE  NATURE  OF  MUSIC 


not  attain  its  highest  development  in  one  voice  until 
it  appears  on  the  eflSlcient  accent  (heavy  rhythm- 
period),  when  it  generates  the  regnant  harmony  of 
the  moment.  This  highest  stage  of  a  tone  in  one 
voice  or  homophony  is  named  briefly,  the  regnant 
stage. 

These  three  stages  apply  exclusively  to  music  in 
one  voice  or  homophony.  Next  let  us  follow  si  3  in 
minor  and  its  major  prototype  ti  3  through  these 
three  stages.  Our  parallel  examples  illustrate  their 
lowest  stage  as  concomitants.  In  minor,  si  is  present 
as  concomitant  3  in  the  harmony  generated  hj  ti  5; 
in  major,  ti  is  present  as  concomitant  3  in  the  har- 
mony of  r^  5.  See  below  at  the  places  marked  by  an 
asterisk. 


Minor 


^ 


Major 


$ 


-(2- 


Next  the  two  tones  appear  as  bytones  in  their 
second  stage. 


Jfinor^ 


^ 


j-XJ  m 


i 


-z^ 


ORIGIN  AND  NATURE  OF  MINOR 
131       153513       1 


195 


Major 


t 


w=^i-r~cj^s. 


Next  in  their  third  and  regnant  stage. 

5        3,        .531 


Minor 


^ 


M 


^ 


t 


m 


3 


Y      *       i  Y 

,       3      5     1. 


i 


^ 


S 


^ 


^^ 


-  F 
3       1 


J 

3      5 


* 
V 


Major 


m 


e 


5      3 

■* a- 


5      1       5      3      13 


I 


11 


-V 


V 


Everywhere  in  all  the  above  and  previous  examples 
the  common  harmonic  self-reports  demonstrate  the 
fundamental  implication  of  rhythm,  therefore  the 
operation  of  the  shaping  principle  of  equilibrium,  in 
short,  the  uniform  laws  of  psychological  causation  in 
homophony. 

The  absence  of  the  diatonic  sol  in  the  minor  group 
of  seven  tones  thus  far  presented  raises  this  question : 


196 


THE  NATURE  OF  MUSIC 


Does  sol  ever  appear  as  a  constituent  tone  of  the 
minor  mode  and  if  so,  how  ?  Presently  we  shall  see 
that  sol  does  appear  in  minor  melodies,  and  plays 
a  most  significant  part  in  the  minor  mode.  The 
succeeding  parallel  examples  present  all  seven  tones 
of  both  modes  in  all  their  tonic  and  dominant  rela- 
tions. 


Major 


Minor 


3     9     1 


3     5      15    3    1     5 


i 


a: 


iM=t 


m 


T=p: 


^m 


V9 

3      8       1 


I 

5 


E3a 


I 


^  These  seven  tones  of  the  minor  group  appear  in 
all  their  tonic  and  dominant  relations  in  each  of  the 
following  fugue-themes  of  Bach. 


3      3     3    1     5    s 


y^-l= 


^m 


mi        la 


78  "87  »1         78"1&S 

H 1  !  1 ! 1     I         I         ,         I »r 


5 


5 


p^-7 


i 


etc 


ORIGIN  AND  NATURE  OF  MINOR  197 


mi       do       la 
/ 


V, 


m 


-=i — s^ 


-=i ^ 


W 


5  6 


'     1   ,    .    5 


*    ± 


££ 


t£ 


6      7 


-^i   5   , 


etc. 


-f^^^^^ 


^m 


V. 


*^ 


^ 


,     5     1 


t 


§te* 


^ 


-^— =^ 


etc. 


The  study  of  Bach  more  than  that  of  any  other 
one  master  quickens  our  perception  of  melohar- 
mony  and  its  common  self-reports  and  teaches  us 
to  appreciate  the  essential  and  fundamental  impor- 
tance of  meloharmonic  discrimination  to  an  intelligent 
interpretation  and  expression  not  alone  of  polyphonic 
music,  but  of  all  music.  In  the  study  of  the  rhythms 
and  harmonies  first  of  one  melody  and  next  of  com- 
bined melodies  we  gradually  realize  that  there  are 
principles  of  expression  inherent  in  music  itself  and 
therefore  in  common  feeling  of  music.  What  these 
principles  are  is  considered  in  a  later  chapter.     That 


198  THE  NATURE  OF  MUSIC 

Bach  had  a  profound  and  vivid  sense  of  these  inherent 
principles  and  expected  as  much  from  his  inter- 
preters may  be  inferred  from  the  fact  that  he  left 
us  his  monumental  piano  work  "The  Well-tempered 
Clavichord"  without  a  single  mark  of  expression. 

We  have  explained  the  origin  in  one  voice  of  the 
minor  form  of  dissonance,  have  defined  its  five  com- 
ponents and  their  correlations.  We  have  accounted 
for  seven  tones  of  the  minor  group  and  have  encoun- 
tered these  seven  tones  in  the  following  nine  minor 
relations :  Za  as  i  of  /,  do  as  3  of  /,  mi  as  6  of  /  and  1  of 
V,  si  as  3  of  F,  ti  as  5  of  F,  re  as  7  of  F,  fa  as  »  of  F 
and  8  of  IV,  All  these  tones  and  relations  appear  in 
the  subjoined  fugue-theme  of  Bach. 

i3i6     siSiSsiSiStIo      It* 


I  JV  I  TTT  7 


46.    Three  Regnant  Minor  Harmonies  and  Their 
Bytones  and  Cadences 

Having  explained  the  subject  of  regnant  harmony 
in  the  preceding  chapter  we  may  proceed  without 
needless  repetitions  to  study  the  bytones  and  cadences 
of  the  minor  tonic,  dominant  and  subdominant  har- 
monies. In  a  given  melody  the  leading  question  is: 
What  is  the  regnant  harmony  or  series  of  regnant  har- 
monies ?  Every  tone  in  a  melody  relates  to  a  regnant 
harmony,  and  if  a  component,  is  classed  a  regnant  tone, 
if  not,  a  bytone.  Such  are  the  essential  points  to  be 
borne  in  mind. 


ORIGIN  AND  NATURE  OF  MINOR 


199 


1.  Regnant  Minor  Tonic,  Its  regnant  tones  are 
lay  do,  mi,  its  bytones  are  si,  ti,  re,  fa.  In  future 
examples  each  bytone  is  marked  by  a  star.  During 
the  regnancy  of  this  harmony,  si,  ti  and  re  report  them- 
selves respectively  as  3,  5  and  7  of  V,  while /a  reports 
itself  as  s  of  iv.  See  below  and  compare  with  the 
parallel  major  example. 


Major 


i 


5  3 


5  1 


5  1 


3  1 


^ 


^m 


W 


■X- 


Minor 


$ 


t^ 


5 


5    1   —  3 


t^ 


B 


H 


M 


■X- 


While  there  are  other  bytones  to  this  regnant  our 
examples  are  strictly  confined  to  the  tone-material 
thus  far  accounted  for.  This  material  includes  the 
diatonic  sol  and  evokes  the  question:  Does  sol  ever 
appear  as  a  bytone  to  this  regnant.^     Our  questions 


200 


THE  NATURE  OF  MUSIC 


are  addressed  not  to  abstract  theory,  but  to  concrete 
melody  and  its  governing  principles.  Melody  could 
and  did,  can  and  does  introduce  sol  in  this  relation 
as  shown  below.  Sol  arises  on  the  line  of  least  resist- 
ance in  the  descending  tetrachord  which  starts  on  the 
octave  and  terminates  on  the  fifth  of  the  regnant 
minor  tonic.  See  last  two  measures  [but  one].  Com- 
parison with  the  parallel  example  in  major  again 
recalls  our  attention  to  the  imitative  nature  of  minor 
and  shows  that  each  harmonic  percept  and  step  in 
minor  are  the  direct  counterparts  of  their  respective 
major  prototypes. 

135      3535      335      3 


Major 


m 


p^ 


^  J.  Ai^T-.^ 


* » 


51335      351     335,35     1 


i 


mm 


3==p: 


1 


* 


*    * 


*  ^ 


* 


Minor 


8         5 


^^ 


^ 


8       3      6 


±=Mz 


*  -3^ 


^^ 


S        1        8        8 


g 


^ 


8      8         5       7       8 


^^ 


W§ 


I 


tr-#- 


^—^ 


■X-   ^ 


^  * 


In  the  minor  example  sol  appears  in  the  last  three 
measures  [but  one],  and  reports  itself  as  small  third  of 
the  dominant,  thus  demonstrating  that  the  minor  domi- 


ORIGIN  AND  NATURE  OF  MINOR  201 

nant  in  this  instance  assumes  the  form  of  a  minor  con- 
sonance,  the  index  of  which  is  v.  The  data  to  be 
observed  in  this  connection  are  first,  that  F  is  a  pure 
diatonic  harmony  since  all  its  components  are  dia- 
tonics;  next,  that  V  arises  spontaneously  in  one  voice; 
next,  that  the  minor  dominant  F  is  a  chromatic  har- 
mony owing  to  its  large  third  si,  which  is  a  chromatic. 
Presently  we  shall  see  that  the  diatonic  minor  domi- 
nant (y)  asserts  itself  in  one  voice  as  a  regnant  har- 
mony. Further  observations  are  these :  The  asterisks 
in  our  examples  show  a  series  of  two  bytones,  the  first 
resolving  into  the  second,  the  second  resolving  into  a 
repose-tone  of  the  regnant  /.  Bytones  which  resolve 
into  the  regnant  harmony  are  classed  as  bytones  of 
the  first  degree:  bytones  of  the  second  degree  resolve 
into  those  of  the  first  degree.  We  shall  meet  with 
bytones  of  the  third  degree  which  resolve  into  those 
of  the  second.  In  the  descending  tetrachord  from 
la  1  down  to  mi  s  we  recognize  the  upper  half  of  the 
descending  melodic  minor  scale  as  follows :  — 


i 


1 


3       3        5 


I 


la       sol   fa    mi       re      do        ti       la 

/ 

All  the  above  tones  are  dia tonics,  yet  the  scale- 
melody  is  not  diatonic.  Why  not  ?  Simply  because 
all  the  harmonies  are  not  diatonic.  To  be  diatonic  all 
the  components  of  a  harmony  must  be  dia  tonics.  This 
is  the  case  with  all  the  tones  of  the  first  of  the  above 
two  tetrachords,  which  is  pure  diatonic  minor.    Not  so 


202  THE  NATURE  OF  MUSIC 

in  the  second  tetrachord,  in  which  the  harmonies  both 
of  re  7  and  ti  5  report  the  presence  of  the  chromatic  si 
(git)  as  a  concomitant  and  component  3,  for  which 
reason  they  are  classed  as  chromatic  harmonies. 
These  common  harmonic  reports  in  one  voice  there- 
fore plainly  and  conclusively  demonstrate  and  prove 
that  even  though  a  melody  be  entirely  composed  of 
diatonics,  yet  that  melody  may  not  be  diatonic.  The 
test  as  to  whether  a  melody  is  or  is  not  diatonic  lies  in 
its  concomitant  harmony,  which  in  one  voice  asserts 
and  reports  itself,  and  this  test  and  new  view-point  will 
greatly  modify  the  facts  and  conclusions  which  in  the 
past  have  been  recorded  by  music-archaeologists  in 
their  studies  of  homophony.  But  is  there  such  a 
thing  as  a  pure  diatonic  minor  melody.^  Such  a 
melody  might  easily  be  conceived  and  represented  by 
selecting  diatonic  chords  as  an  accompaniment,  but 
this  would  be  but  an  arbitrary  conception  void  of  any 
archaeological  value.  On  the  other  hand,  if  such  a 
melody  is  conceivable  in  one  voice  and  itself  generates 
and  reports  only  diatonic  harmonies  which  we  all  per- 
ceive in  common,  then  indeed  would  we  gain  a  fact  of 
considerable  value  to  music-archseology  and  psycho- 
logy. The  common  self-reports  in  the  next  illustration 
answer  our  question  in  the  affirmative,  and  conclusively 
demonstrate  that  such  melodies  do  arise  in  one  voice, 
and  from  this  we  may  infer  that  they  may  have  arisen 
in  the  remote  homophonic  past. 

1  Sfi  36  8         1  81  6        1888 


umi^ 


•x-  ^ 


ORIGIN  AND  NATURE  OF  MINOR 


203 


This  is  a  "pure  minor  melody,  each  tone  reports  a 
diatonic  harmony,  each  harmony  is  a  minor  conso- 
nance. In  the  first  measure  the  by  tone /a  reports  itself 
3  of  IV,  in  the  second  measure  sol  reports  itself  s  of  F, 
in  the  third  measure  both  bytones  make  the  same  re- 
ports. Thus  through  sol  the  minor  dominant  assumes 
the  form  of  a  minor  consonance.  Thanks  to  self- 
asserting  harmony  in  one  voice  we  are  able  to  aflSrm 
that  there  is  such  a  thing  as  "pure  diatonic  minor  which 
is  the  perfect  counterpart  of  jmre  diatonic  major.  The 
subject  of  pure  minor  melodies  will  again  be  reverted 
to  when  we  shall  study  sol  in  other  relations. 

Does  melody  ever  ascend  on  the  upper  half  of  the 
descending  melodic  minor  scale  ?  Yes,  there  are  many 
examples,  especially  in  modern  music.  We  cite  one 
from  Liszt,  Rhapsody  II. 


Si; 


etc. 


m^ 


mi    fa       sol 


The  ascending  upper  half  or  tetrachord  of  the 
melodic  minor  scale  has  been  derived  through  imita- 
tion from  the  same  tetrachord  of  the  major  scale,  thus 
introducing  another  chromatic,  namely,  fi  (f jlf  in  A 
minor)  as  follows:  — 


Major 


c±r 

1 

5 

3 

7 
\ — 

5 

H— 

3   3    1 

3 

— # — 

-W- 

1— J — 

P — 

— n^ — 

*  * 

I    1 

204 


THE  NATURE  OF  MUSIC 


^    ^ 


Minor 


$ 


B: 


3  3 


f-pf 


m 


*  * 


3    3 


3    3 


i^zt^j-^-^BE^^^tJ^^-^^ 


Here  the  chromatic  fi  (ijjf)  arises  as  a  bytone  to 
regnant  / ;  it  is  a  bytone  of  the  second  degree  and 
resolves  into  si,  a  bytone  of  the  first  degree ;  its  report 
of  3  announces  the  subdominant  in  the  form  of  a  major 
consonance.  Our  examples  show  that  the  minor 
dominant  in  one  voice  assumes  the  forms  of  both  con- 
sonances, the  major  form  through  si  3,  the  minor  form 
through  sol  a.     See  below. 

13       5  a        .        . 

mi  —  si  —  ti  I  mi  —  sol 


V  \n 

Next  we  note  that  in  one  voice  the  minor  subdomi- 
nant assumes  both  forms,  the  minor  through /a  s,  the 
major  through  fi  3. 


8 

-fa 
IV 


3     5 

-fi  — la 

Iv 


ORIGIN  AND  NATURE  OF  MINOR  205 

We  have  met  all  these  forms  as  byharmonies  to  reg- 
nant /  and  are  presently  to  see  how  they  arise  as  reg- 
nants.  All  these  harmonies  are  nearest  related  to  the 
minor  tonic,  and  arose  at  an  early  period  of  melody's 
exploitation  of  the  minor  mode  in  one  voice ;  and  since 
they  assume  both  the  major  and  minor  forms  and 
appear  both  as  diatonic  and  chromatic  harmonies, 
they  plainly  reveal  the  mixed  or  hybrid  composition  of 
the  minor  mode,  and  add  further  conclusive  testimony 
to  the  derived  and  imitative  nature  of  minor.  Our 
examples  and  analyses  clearly  point  out  that  there  is 
but  one  source  of  light  and  truth  on  homophonic  prob- 
lems, that  there  is  but  one  true  and  responsible  reporter 
on  those  fundamental  homophonic  harmonies  in 
which  all  harmonies  are  rooted,  the  one  and  only  re- 
porter into  whose  testimony  the  personal  equation 
cannot  enter.  This  one  source,  this  one  reporter  is 
melody,  the  composite  of  rhythm  and  harmony,  the 
free,  untrammeled  and  universal  rhythmo-harmonic 
voice  of  music.  The  growth  of  the  scale  of  tones  from 
its  incomplete  to  its  complete  diatonic  form,  thence  to 
its  chromatic  form  and  thence  to  its  present  enhar- 
monic form,  means  the  gradual  growth  of  the  tone- 
system  from  its  first  beginnings  up  to  the  present  time. 
However,  the  efficient  cause  of  all  this  growth  is 
rhythmo-harmonic  melody.  Under  the  guidance  and 
government  of  its  inherent  laws  of  development 
melody  discovered  and  exploited  tone  upon  tone,  re- 
lation upon  relation,  harmony  upon  harmony,  thus 
gradually  expanding  the  scale  and  system  of  tones  and 
keys.  Beginning  by  intoning  the  relation  of  cadence 
and  repose  and  generating  consonance  and  dissonance, 


£06 


THE  NATURE  OF  MUSIC 


melody  has  continued  to  cadence  and  repose  on  this 
tone,  on  that  tone,  on  any  tone  in  the  ever  widening 
tone-realm,  the  difference  between  to-day  and  yester- 
day being  a  difference  in  the  extent  of  the  tone-realm, 
a  difference  between  simpler  and  more  complex  melo- 
dies. Like  yesterday,  so  to-day  melody  reports  now  a 
consonance,  now  a  dissonance,  no  more,  no  less. 

2.  Regnant  Minor  Dominant,  Like  its  major  pro- 
totype this  regnant  has  three  forms:  a  three-tone 
form  F,  a  four-tone  form  F^,  a  five- tone  form  Fg.  This 
harmony  was  first  reported  in  melody  by  its  fifth  ti. 
The  concomitants  of  ti  5  are  mi  1  and  si  3.  The 
efficient  accent  on  ti  or  si  generates  regnant  F  thus :  — 


i 


i 


I 


p^ 


Through  its  accession  of  this  regnant,  melody  was 
enriched  first  by  all  the  possible  steps  from  one  compo- 
nent to  another,  next  by  the  bytones  and  cadences 
playing  upon  its  components.  The  former  are  too 
obvious  and  require  no  illustration.  As  to  the  latter 
we  will  first  consider  the  bytones  of  regnant  F.  Reg- 
nant F  has  but  two  diatonic  bytones,  namely,  la  and 
do,  which  cadence  into  the  third  (si)  and  fifth  (ti)  of 
this  regnant.  See  below  and  compare  with  parallel 
example  in  major. 


3     13131535151311 


Major 


ORIGIN  AND  NATURE  OF  MINOR 
8      1    3i3i    SaSi    5i31i 


207 


Minor 


F* 


There  are  no  diatonic  bytones  to  the  root  (mi)  of 
this  regnant.  Re  and  fa,  which  lie  respectively  under 
and  over  this  root,  are  not  bytones  of  the  regnant  domi- 
nant ;  they  are  components  and  regnant  tones.  During 
the  regnancy  of  the  dominant,  re  reports  itself  as  i  and 
gives  rise  to  the  four-tone  form  V^  while  fa  reports 
itself  as  o  giving  rise  to  the  five-tone  form  Fg.  See 
below  and  compare  with  corresponding  tones  and 
relations  in  major. 


«)        5      31357      5313579 


^ 


V9 


Major 


t  1^   u 


Minor 


b) 


5      3     1     357      531357    » 


1     5 


Uajor    Jf       I         I 


C)7 


V9 


9     5     13 


i 


6) 


1     5 


e), 


5     1 


i 


208 


THE  NATURE  OF  MUSIC 


The  seventh  (re)  of  V^  has  but  one  diatonic  bytone, 
which  lies  under  it  and  is  do.  The  diatonic  lying  over 
re  7  is  mi  the  regnant  root.  See  below  and  compare 
with  parallel  major. 

5      31        7     3    5     S     7    B   7    1    S 


i 


:^ 


Major 


B^ 


I 


h^ 


V,  * 


•X- 


Minor 


i 


m 


E3 


tEEEEi 


'  7 


1 


Next  let  us  study  the  ninth  (fa)  of  Vq.  In  the  first 
place  this  small  ninth  like  its  prototype  la  9  in  major, 
cadences  into  the  regnant  harmony  of  which  it  is  a 
component.  In  other  words,  the  regnant  tone  fa  o 
resolves  into  its  co-harmonic  the  regnant  tone  mi,  as 
shown  below.     Again  compare  with  example  in  major. 

7     5     3     9         13     5-^        ^ 

Major 


13     5 


g 


Minor 


3 


fcfti 


During  the  regnancy  of  the  dominant,  melody  also 
resolves  the  ninth  upward  into  the  upleader,  which  is 
the  third  of  that  harmony.  Compare  the  next  parallel 
illustrations.     This  rising  cadence  is  keenly  felt  in 


ORIGIN  AND  NATURE  OF  MINOR 


209 


stepping  from  the  large  ninth  to  the  upleader  {la  to  ti 
in  major, /z  to  si  in  minor  as  at  b)  in  the  minor  example 
below),  but  is  not  perceptible  in  stepping  from  the  small 
ninth /a  to  the  upleader  si  as  at  a)  in  the  minor  ex- 
ample. 


Major 


i 


5    3  1 


IS^^ 


5  V   9    3   1 

— 0 


? 


^- 


I 


6)5 


9    3 


^^ 


Minor 


s 


tm 


■z?- 


V 


^U 


At  a)  in  the  above  minor  example,  fa  and  the  other 
components  of  regnant  V  are  the  counterparts  in 
minor  of  the  corresponding  components  of  regnant  V 
in  the  major  example.  But  at  6)  in  the  minor 
example  the  melody  during  the  regnancy  of  V  exactly 
imitates  and  duplicates  the  steps  of  the  major  melody 
in  the  corresponding  measure  thus  introducing  the 
chromatic  fi  (/jlf),  which  reports  itself  as  large  ninth 
and  a  component  of  the  regnant  harmony,  thereby 
causing  the  regnant  minor  dominant  to  assume  the 
original  major  form  of  dissonance.  This  inherent 
tendency  of  both  the  large  and  small  ninths  to  resolve 
each  into  the  harmony  of  which  it  is  a  component  has 
led  some  music-theorists  to  class  the  ninth  as  a  bytone 
to  the  chord  of  the  dominant.  But  here  we  are  not 
dealing  with  chords,  we  are  dealing  with  the  antece- 
dents of  chords,  with  harmony  in  one  voice  the  com- 
mon self-reports  of  which  for  the  first  time  enable 


210 


THE  NATURE  OF  MUSIC 


us  to  discriminate  positively  between  regnant  tones 
and  by  tones,  and  they  clearly  and  conclusively  demon- 
strate in  the  case  of  the  two  ninths  that  a  tone  may  be 
at  once  a  regnant  tone  and  in  cadence  to  its  own 
harmony.  A  regnant  tone  is  not  a  bytone,  a  bytone 
is  not  a  regnant  tone:  by  carefully  and  strictly  ad- 
hering to  the  necessary  distinction  between  the  two 
we  shall  avoid  what  else  would  be  inextricable  con- 
fusion. 

Are  there  any  diatonic  bytones  to  either  of  the 
two  ninths  during  the  regnancy  of  either  of  the  two 
dominants?  No,  the  tones  thus  far  accounted  for 
which  lie  over  and  under  the  ninth  are,  like  the 
ninth,  components  of  the  regnant  dominant  in  both 
modes.  The  tone  under  the  ninth  is  the  root,  the 
tone  over  the  ninth  is  the  third  of  the  dominant, 
during  the  regnancy  of  which  both  tones  are  of 
course  regnant  tones.  We  are  now  to  see  that  the 
ninth  is  not  the  only  cadencing  regnant  tone  as  shown 
at  N.B.  in  the  next  parallel  examples,  in  which  the 
melody  cadences  from  the  regnant  third  to  the  regnant 
ninth. 


35739   1   91391357399    1 


^    Y-^   N.B.  N.B.      ~^ 


Major 


V-A- 


3  5 


7     3     9 


l8ol3578       9      0        1 


^^^^^^M 


Minor 


N.B. 


N.B. 


N.B. 


ORIGIN  AND  NATURE  OF  MINOR  211 

The  diatonic  sol  at  each  N.B.  in  the  above  minor 
melody  calls  for  a  series  of  observations.  Through 
sol  in  the  above  relation,  original  harmony  in  one 
voice  discloses  a  curious  and  interesting  fact  which 
throws  a  strong  and  clear  light  upon  consequent 
complex  chord-formations  so  numerous  in  modern 
music.  The  above  minor  melody  is  the  exact  coun- 
terpart in  minor  of  the  parallel  melody  in  major,  and 
sol  arises  in  the  minor  melody  on  the  line  of  least 
resistance.  Previously  we  met  sol  as  small  third  but 
as  a  by  tone  to  regnant  /.  Now  we  meet  sol  again  as 
a  small  third,  but  this  time  as  a  regnant  tone  and, 
what  is  more,  as  a  regnant  tone  in  cadence.  Observe 
that  the  cadence-tend  of  sol  in  this  relation  is  much 
stronger  than  that  of  the  parallel  tone  ti  in  the  major 
melody.  And  why  ?  Because  of  the  presence  of  the 
large  third  si  in  the  concomitant  harmony  of  sol. 
That  is  to  say,  this  sol  a  reports  si  3  in  its  concomitant 
harmony,  it  means  that  we  feel  and  hear  the  small 
third  and  the  large  third  of  the  same  root  simulta- 
neously. Hence  the  stronger  cadence- tend  of  sol  s  to 
fa  9  than  that  of  the  parallel  major  ti  3  to  la  9.  Hence 
the  important  fact  reported  by  harmony  in  one  voice 
that  there  are  harmonies  containing  double  thirds^ 
that  is,  two  thirds  of  one  root.  Hence  the  inference 
that  there  may  be  other  double  harmonics  as  double 
fifths  and  the  like,  an  inference  to  be  verified  later. 
From  this  important  fact  adduced  from  and  verified 
by  harmony  in  one  voice  we  naturally  draw  the 
logical  conclusion  that  chords  may  be  compounded 
of  double  harmonics,  that  is,  of  double  thirds  and  the 
like.     Such   chords   may  be  named   double  chords. 


212 


THE  NATURE  OF  MUSIC 


They  are  a  true  reality,  since  modern  music  has  intro- 
duced them  frequently.  I  present  a  double  chord 
containing  double  thirds,  choosing  for  my  subject  sol  s 
in  the  above  relation,  which  tone  and  relation  are 
responsible  for  the  genesis  of  this  double  harmony 
and  consequent  double  chord. 

1       1 


This  cadence  of  sol  z  into  fa  ©  during  the  regnancy 
of  V  is  often  found  in  the  melodies  of  Chopin.  Here 
is  a  familiar  example  from  the  prelude  in  E  minor. 

1  sDoloOsols 


i 


^ 


w 


il 


'^^=¥ 


N.B. 


etc. 


5* 


I 


lEI 


*-^ 


17 


Such  excerpts  from  compositions  might  be  multi- 
plied indefinitely.  For  my  last  illustration  of  sol  • 
in  this  relation  I  give  the  principal  theme  of  the 
allegro  of  Beethoven's  sonata  op.  111.  Although  this 
opening  theme  presents  sol  s  but  once,  it  is  given  in  its 
entirety,  it  being  so  fine  an  example  of  harmony  in 


ORIGIN  AND  NATURE  OF  MINOR 


213 


one  voice,  a  form  of  writing  in  which  Beethoven  so 
frequently  expressed  himself. 

sSSl  8  3  fioSl  8  3  O 


assi 


'TTA0rT^ 


m 


I7       8      5      STsSl       ol 


7       8      O      8   7    8 


1    »    1 


7        8       7        8 


5       8       7       8       5 


15         7 


^i 


^J    *    J 


hj.    J    J.  J.  i    ^    -i  -J-    :;^ 

T  "•* 


^ 


.    5 


5    1    3 


S^ 


^ 


^ 


^  '  ^  ^ 


T*— •^ 


T- 


8       5 


5   1 


1       6 


3    9    1   5    1     3 


7         8 


:^3 


^ 


5=rf 


^m 


s^ 


-JK 


t=t: 


iF 


§a 


J       ^''      /J       F 

5      o      It      5i37a5ol75i3 


fe£ 


i=? 


tr* 


t^it 


s 


•— # 


tK 


5  1 


* — • — wr 


1 


'-   etc. 


214  THE  NATURE  OF  MUSIC 

The  above  harmonic  numbers  indicate  the  self- 
report  of  each  tone  and  speak  for  themselves.  This 
theme  presents  certain  regnant  harmonies  which 
hitherto  have  not  appeared  in  our  examples,  and 
comment  upon  which  at  this  juncture  of  our  exposi- 
tion would  be  premature  and  is  therefore  deferred. 
In  connection  with  the  above  example  we  call  atten- 
tion to  this  law.  Relation  of  tones  and  harmonies  is 
always  forward.  Rhythm-relation  being  forward  all 
relation  is  forward.  Observe  the  triplet  in  each  of 
the  two  motives  with  which  the  theme  opens.  This 
premeasural  triplet  relates  forward  and  therefore 
relates  to  and  plays  upon  the  regnant  tonic-harmony. 
Observe  fa  (a^)  at  the  end  of  the  third  and  fourth 
measures:  it  likewise  relates  forward  and  therefore 
reports  itself  9  of  F. 

One  more  remark  remains  to  be  made  regarding 
sol  8  as  a  cadencing  regnant  tone.  It  is  an  original 
product  of  the  minor  mode  and  is  distinctively  a 
minor  harmonic  percept.  We  have  seen  how  melody 
evolved  the  minor  mode  out  of  tone-material  and 
relations  previously  extant  in  major,  thus  generating 
the  new  and  individual  minor  forms  of  consonance 
and  dissonance  by  imitating  the  cadence  and  repose 
relations  of  the  prototype  major  mode.  Through 
the  same  process  of  imitation,  melody  has  reversed 
the  process  by  reproducing  and  imitating  in  major 
many  of  the  melodic  steps  and  harmonic  forms  which 
first  arose  in  minor.  Just  as  melody  adopted  the 
major  tetrachord  in  minor  (below  at  a))  just  so 
melody  adopted  two  minor  tetrachords  in  major,  as 
at  b)  and  c). 


ORIGIN  AND  NATURE  OF  MINOR  215 

o)  h)  e) 


Major 


a) 


Minor 


This  introduction  by  melody  of  the  products  of  one 
mode  into  the  other  at  once  exhibits  the  union  in 
melody  of  perfect  freedom  with  perfect  adherence  to 
law  and  order,  but  in  modern  music  has  assumed  such 
proportions  and  created  such  an  apparent  modal 
muddle  that  each  of  the  two  modes  seems  well-nigh 
to  have  lost  its  identity.  The  modal  identity  is  how- 
ever always  asserted  and  reported  by  the  modal 
major  or  minor  tonic-consonances.  This  self-report 
so  obvious  and  definite  in  simple  homophonic  melo- 
dies is  less  obvious  but  not  less  definite  in  the  com- 
plex melodies  of  polyphony  and  chorded  music  with 
their  intricate  chromatic  harmonies  and  manifold 
modulations.  As  we  progress  in  tracing  the  evolution 
of  melody  and  the  consequent  concurrent  evolution 
of  tonality  and  of  the  tone-system,  it  will  become 
increasingly  clear  that  our  conceptions  of  mode, 
tonality  and  scale  or  system  require  considerable 
modification.  In  order  to  maintain  our  clearness  of 
view  as  we  gradually  enter  into  these  apparent  com- 
plexities we  will  continue  to  focus  our  attention  upon 
melody,  the  voice  which  has  gradually  discovered  and 
exploited  the  wide  realm  of  tones  as  represented  by 
the  enharmonic  scale  with  its  boundless  potential 
relations  and  harmonies,  our  only  source  and  reporter 


216 


THE  NATURE  OF  MUSIC 


of  truth.  I  repeat,  melody,  perfectly  free  because 
perfectly  self-governed,  raay  repose  or  cadence  here, 
there,  anywhere  in  the  tone-realm.  Melody  exercised 
this  freedom  yesterday  in  a  narrow,  exercises  it  to-day 
in  a  wide  realm  of  tones. 

One  more  form  of  the  regnant  minor  dominant 
remains  to  be  presented.  This  form  is  a  minor  con- 
sonance generated  by  melody  through  the  diatonic 
sol.  We  have  met  this  consonance,  due  to  the  report 
of  sol  as  small  third,  in  the  paragraph  on  the  minor 
tonic,  where  sol  appeared  as  a  bytone.  In  the  follow- 
ing melody  sol  a  is  a  regnant  tone  and  announces  the 
regnant  minor  dominant  in  the  form  of  a  minor 
consonance. 


m 


5  1 

~N 


1       8 


^ 


i^ 


3     6 


8     5 


^^ 


-^ 


it=i=!t=iiz^ 


IV 


Here  sol  a  reports  regnant  v  in  the  second,  third 
and  fourth  measures  and  appears  as  a  bytone  in  the 
fifth  and  last  measures.  This  melody  reports  three 
diatonic  harmonies,  namely,  7,  V  and  iv  ;  all  of  its  tones 
and  their  concomitant  harmonics  are  diatonics,  all 
its  harmonic  percepts  are  minor,  in  short,  this 
example  presents  a  jpure  diatonic  minor  melody. 
This  proof  by  the  above  harmonic  self-reports  that 
a  pure  minor  melody  is  not  only  conceivable  and 
self-assertive  in  one  voice,  but  is  an  absolute  reality. 


ORIGIN  AND  NATURE  OF  MINOR 


217 


confirms  our  thesis  that  melody  and  not  a  scale  is  the 
real  object  of  study  and  source  of  true  knowledge 
regarding  music.  No  conceivable  rhythmic  arrange- 
ment in  one  voice  of  the  scale  of  diatonics  from  la  to 
la  will  generate  and  report  exclusively  diatonic  har- 
monies and  minor  consonances.  To  be  sure  this  is 
easily  effected  with  chords  arbitrarily  selected  for  the 
purpose,  but  such  selective  representation  of  harmony 
is  no  test. 

The  form  of  a  minor  consonance  cannot  be  gener- 
ated by  the  other  two  components,  namely,  the  root 
(mi)  and  the  fifth  (ti),  save  when  both  or  either  of 
the  two  is  associated  in  the  same  rhythmic  period 
with  sol  3.  This  is  shown  in  our  next  example  from 
the  fifth  measure  onward.  Ti  alone  (see  second 
measure)  or  ti  supported  by  mi  (see  third  measure) 
always  announces  the  minor  dominant  in  the  form 
of  the  major  consonance. 


1       5 


6        S       1 


^Efe^ 


§^ 


F- 


The  mixed  or  hybrid  nature  of  the  harmonies  gen- 
erated by  the  diatonics  of  the  minor  mode  is  next 
exemplified,  and  may  suggest  the  rich  and  varied  har- 
monic potentiality  of  the  minor  mode  to  the  tone-muse 
of  young  composers. 


218 


THE  NATURE  OF  MUSIC 


"5V 

-*- 

— F- 

• 

5 

-ft- 

-^ 

6       8 

-a— f- 

1 

s 

ft 

7    5 

-s — h- 

-^  K 

L 

1 

.  i^ 

=r+- 

-h 

._iL 

=1= 

+-^ 

8         18         1 


5ll  81585  i 


9 


9fc?=? 


^^^ 


During  the  regnancy  of  F,  sol  the  generator  of  this 
harmony   has   one   diatonic   by  tone,  namely,   la^  as 


follows :  — 

1=1 


3    18 


S      1 


I 


#-1^ 


8    15    18    1       1 


^^§ 


1=0: 


rt: 


e 


The  summary  of  the  forms  of  the  regnant  minor 
dominant  which  we  have  thus  far  generated  and  ex- 
plained is  as  follows:  Fg,  F9,  F,,  F,  v, 

3.  Regnant  Minor  Subdominant  Like  its  major 
prototype  this  regnant  was  first  generated  and  an- 
nounced in  melody  by  its  third  which  is  fa.  The  effi- 
cient accent  on  fa  and  also  on  re  when  supported  by /a 
generates  this  regnant  minor  consonance  and  diatonic 
harmony  as  follows :  — 


^ffif  iff^if  fife-J4 


18      5 


^ 


^# 


ir 


JV 


IV 


Our  present  tone-material  contains  five  bytones  to 
this  regnant.     Four  of  these  bytones  are  diatonics, 


ORIGIN  AND  NATURE  OF  MINOR 


219 


namely,  do,  mi,  sol,  ti.  The  other  by  tone  is  the  chro- 
matic si.  The  next  example  includes  all  of  them  and 
indicates  the  harmonic  self-report  of  each  in  this 
specific  relation. 


IV- 


f^-^ 


S      S      t      1     5     1 


5     8     5     S     1 


a    1 


^ 


i 


=9fc^3 


^ 


^ 


f 


•"sflt- 


The  efficient  accent  onfi  (f^  in  A  minor)  causes  the 
regnant  minor  subdominant  to  assume  the  form  of  a 
major  consonance.  Owing  to  the  chromatic^  (f|t) 
this  regnant  IV  is  classed  as  a  chromatic  harmony 
which,  as  the  next  example  shows,  enters  most  natu- 
rally after  regnant  /  and  is  most  naturally  succeeded  by 
regnant  V  or  regnant  iv. 


^=M 


^S 


^ 


IV 


5^ 


£=t 


3    3    3    3    9    3 


^S=:j^»     #     ■     P 


I  n   L  I 


IV       ,y 
5 


IV 
3    3    3  5 

6  ,.  .8,8858  1 


^>^j=£^^ftf^^?^#^^^^^ 


IV  * 


ir 


220  THE  NATURE  OF  MUSIC 

Here  we  note  that  regnant  IV  enters  after  /  and  is 
succeeded  twice  by  V  and  twice  by  iv.  A  bytone  to 
regnant  IV,  namely,  si  (gjjf),  appears  in  the  triplets  and 
is  marked  by  an  asterisk.  Our  present  tone-material 
contains  other  bytones  to  this  major  form  of  the  sub- 
dominant,  and  even  though  all  these  bytones  are  dia- 
tonics  they  all  have  a  modulatory  tendency,  that  is, 
they  shift  the  key-centre  and  change  the  mode  from 
minor  to  major.  We  have  demonstrated  that  even 
though  a  melody  be  composed  entirely  of  diatonics  it 
may  contain  and  report  chromatic  harmonies,  and  we 
are  presently  to  show  how  diatonics  among  themselves 
may  effect  and  definitely  report  modulations.  Mean- 
while, let  us  observe  that  the  fact  that  a  melody  con- 
tains only  diatonics  by  no  means  proves  a  melody  to 
be  diatonic.  To  the  eye  such  melodies  on  paper  ap- 
pear to  be  diatonic  and  have  been  thus  erroneously 
judged  and  classified.  Thanks  to  common  harmonic 
reports  in  one  voice  such  errors  are  no  longer  possible. 
The  statement  that  music  is  heard,  not  seen,  ought  to 
be  supererogatory.  An  Indian  chief  after  having  in- 
vited a  group  of  men  to  squat  with  him  in  his  wigwam 
proceeded  to  ask  what  was  the  vocation  of  each  guest. 
Fixing  his  eyes  upon  one  who  was  pointed  out  as  a 
musician  the  chief  placed  a  finger  on  his  ear  and 
winked.      That  much  he  knew. 

We  have  now  presented  the  regnant  harmonies  of 
the  minor  tonic,  dominant  and  subdominant,  and  have 
studied  the  bytones  and  cadences  of  each.  The  rela- 
tions and  combinations  of  regnant  harmonies  among 
themselves,  their  progressions  and  resolutions  (ca- 
dences), were  analyzed  in  the  preceding  chapter  where 


ORIGIN  AND  NATURE  OF  MINOR 


221 


we  treated  the  regnant  harmonies  in  major.  Those 
in  minor  being  very  similar  in  their  relations  and  suc- 
cessions, we  need  not  pause  here  to  consider  them  in- 
dividually since  their  relations  and  connections  are 
exemplified  in  our  illustrations  of  minor  melodies.  To 
summarize.  The  tone-material  which  has  thus  far 
appeared  in  our  minor  melodies  aggregates  nine  tones, 
namely,  the  seven  diatonics  and  the  two  chromatics 
si  and  fi  (^  and  fjj!  in  A  minor).  Our  next  example 
introduces  all  of  these  tones. 


^ 


7 


Ui 


^- 


^ 


3     9 


=9i§: 


^=W 


V 


^' 


4-  I 


t=t 


*i 


*f-fyi' 


I 


:P=1= 


-•— s>- 


Next  we  summarize  the  forms  of  harmonies  thus 
far  reported  by  our  melodies  in  minor. 

1.  Minor  consonances:  /,  iv,  v.  i  is  the  original, 
IV  and  V  are  duplicates. 

2.  Major  consonances:  F,  IV.  Both  are  dupli- 
cates of  the  original  I  or  major  tonic. 

3.  Four-tone  dissonances:  F^,  which  is  a  dupli- 
cate of  the  major  prototype  V^. 

4.  Five-tone  dissonances:  F^,  F9.  The  latter  is  a 
duplicate  of  the  original  major  V9. 

All  the  above  forms  resolve  themselves  into  two 
which  had  their  origin  in  the  minor  mode  and  which 
are  distinctively  minor,  namely,  the  minor  form  of 


222  THE  NATURE  OF  MUSIC 

consonance,  that  based  on  la  being  the  original;  the 
minor  form  of  dissonance,  that  based  on  mi  being  the 
original. 

47.   Harmonic  Percepts  of  Minor  Origin 

The  minor  forms  of  consonance  and  dissonance 
comprise  five  harmonic  percepts  which  correspond  to 
the  five  major  percepts  derived  from  the  major  forms 
of  consonance  and  dissonance.  Both  groups  are 
given  below  for  comparison,  and  each  harmonic  per- 
cept is  indicated  over  the  tone  on  which  melody  first 
generated  and  reported  it. 

13    5         7  9 

1.  Percepts  in  Major:     do    mi    sol  fa    la 


2.  Percepts  in  Minor:  I  la    do    mi  re    fa 

^  V 

Among  these  percepts  we  observe  one  duplicate, 
the  small  seventh,  which  originated  in  major  on  fa 
and  which  was  reproduced  in  minor  on  re.  Thus 
only  four  of  these  percepts  had  their  origin  in  minor 
and  are  therefore  distinctively  minor  harmonic  per- 
cepts.    They  are :  — 

I860 

la     do     mi    fa 

The  whole  number  of  harmonic  percepts  thus  far 
generated  by  melody  and  explained  is  nine,  as  follows : 

1,  i;  3,  3;  5,  5;  7;  9,  9. 


ORIGIN  AND  NATURE  OF  MINOR  223 

The  meaning  and  use  of  these  numbers  we  have 
defined.  Over  the  notes  of  a  melody  they  are  read 
thus:  large  root,  small  root;  large  third,  small  third; 
large  fifth,  small  fifth;  small  seventh;  large  ninth, 
small  ninth. 

The  self-reports  of  melodies  in  minor  like  those  in 
major  confirm  the  truth  of  our  theses,  namely,  that  in 
one  voice  each  tone  is  felt,  heard  and  expressed  in 
cadence  or  repose  as  root  or  third  or  fifth  or  seventh 
or  ninth ;  that  specific  relations  generate  specific  forms 
of  harmony,  and  that  the  two  are  linked  as  cause  and 
effect;  that  no  form  of  harmony  contains  more  than 
five  components.  These  nine  percepts  derived  from 
the  major  and  minor  forms  of  consonance  and  dis- 
sonance, and  which  are  the  harmonic  products  of 
homophonic  melody  far  back  in  the  ages,  constitute 
the  connecting  link  between  homophony  on  one  hand 
and  polyphonic  and  chorded  music  on  the  other,  and 
therefore  the  harmonic  basis  of  all  music.  However 
simple  the  one  or  complex  the  other,  one  thing  is 
always  true  of  and  reported  by  all  one-voice  music 
and  all  multi-voice  music.  It  is  this.  Now  the  reg- 
nant harmony  is  a  consonance,  now  it  is  a  dissonance, 
one  or  the  other.  This  was  so  in  the  yesterday,  is  so 
in  the  to-day,  and,  we  may  assume,  will  be  so  in  the 
to-morrow  of  music's  evolution.  Homophonic  mel- 
ody produced  the  only  two  forms  of  consonances  in 
music  and  the  two  original  major  and  minor  forms  of 
dissonances.  All  the  above  nine  harmonic  percepts 
are  therefore  distinctively  homophonic  products.  As 
we  shall  see,  homophonic  melody  may  have  continued 
to  produce  even  other  harmonic  percepts  of  the  dis- 


224  THE  NATURE  OF  MUSIC 

sonant  order,  to  which  belong  all  the  myriad  new 
harmonic  percepts  and  forms  which  are  distinctively 
the  products  of  polyphonic  and  chorded  music.  All 
the  new  harmonic  percepts  derived  from  multi-voice 
music  are  inseparably  linked  to  and  rooted  in  the 
above  nine  and,  as  we  shall  find,  are  either  combina- 
tions, compounds  or  modifications  of  the  nine.  Hence 
the  importance  of  the  nine.  In  pursuing  this  study  of 
melody's  evolution  of  harmony  which  we  trace  in  its 
common  self-reports  two  things  should  be  borne  in 
mind :  first,  the  harmonic  percept,  important  because 
it  comprises  a  complete  harmonic  thread ;  next,  the 
regnant  harmony,  important  because  it  determines 
the  exact  relations  of  tones. 

48.   A   Tone's  Harmonic  Pedigree 

Observe  that  each  of  the  above  nine  percepts  arose 
on  a  specific  tone;  next,  that  these  percepts  are  repro- 
duced on  other  tones ;  next,  that  certain  percepts  when 
thus  reproduced  on  certain  tones  generate  new  tones 
in  the  concomitant  harmony.  For  example,  sol  was 
the  first  large  fifth,  namely,  5  of  I  in  major.  When 
this  large  fifth  was  reproduced  on  ti  in  minor  a  new 
tone,  the  chromatic  si,  was  generated  in  the  concomi- 
tant harmony,  in  which  it  reported  itself  as  large  third. 
This  fact,  in  conjunction  with  the  thesis  that  all  the 
nine  percepts  are  potential  in  all  tones  and  with  the 
rhythmo-harmonic  laws  of  causation  which  we  have 
set  forth,  throws  light  upon  the  processes  by  which 
melody  gradually  expanded  the  tone-system  and  tonal- 
ity and  evolved  so  much  out  of  so  little.  But  the  fact 
that  a  harmonic  percept  originated  on  a  specific  tone 


ORIGIN  AND  NATURE  OF  MINOR  225 

and  thereafter  was  reproduced  on  other  tones  points 
to  the  interesting  inference  that  each  tone  has  a  har- 
monic pedigree.  By  this  I  mean  that  melody  first  in- 
troduced a  tone  in  a  specific  relation,  and  next  pro- 
ceeded to  introduce  that  tone  in  another  relation  and 
then  in  another,  and  so  on.  Such  a  sequence  of  rela- 
tions would  trace  the  tone's  harmonic  evolution  or 
line  of  descent.  Aside  from  its  immediate  interest 
and  value  to  psychology,  the  harmonic  pedigree  if  as- 
certained would  enable  the  archseologist  to  determine 
approximately  the  chronological  order  and  relative 
ages  of  primitive  melodies.  To  be  explicit.  What  is 
a  specific  tone's  line  of  descent  or  harmonic  pedigree  ? 
It  is  that  tone's  evolutionary  sequence  of  harmonic 
relations.  Where  is  this  evolutionary  sequence  to 
be  traced?  In  melody,  where  it  was  produced. 
All  harmonic  percepts  being  potential  in  all  tones, 
melody  has  carried  each  tone  through  a  sequence 
of  percepts.  To  illustrate  all  this  we  will  here  pre- 
sent the  harmonic  pedigrees  of  the  seven  original 
tones  (diatonics)  so  far  as  ascertained  at  this  junc- 
ture of  our  study. 

1.  Do  first  arose  as  1  of  I  in  major,  then  appeared 
as  5  of  IV  in  major,  then  as  s  of  /  in  minor.  So  far  as 
already  ascertained  the  pedigree  of  do  is  briefly  1,  5,  3. 

2.  Sol  first  arose  as  5  of  I  in  major,  next  appeared 
as  1  of  V  in  major,  then  as  a  of  r  in  minor.  This 
pedigree  of  sol  is  briefly  5,  1,  s. 

3.  Mi  first  arose  as  3  of  I  in  major,  next  appeared 
as  5  of  /,  1  of  F  and  i  of  F  in  minor.  This  pedigree  is 
briefly  3,  s,  1,  i. 

4.  Re  began  as  5  of  V  in  major,  next  appeared  as  i 


226  THE  NATURE  OF  MUSIC 

of  V  in  minor,  then  as  i  of  IV  and  1  of  IV  in  minor. 
This  pedigree  is  5,  ?,  i,  1. 

5.  La  began  as  3  of  IV  in  major,  next  appeared  as 
9  of  V  in  major,  then  as  i  of  /,  5  of  iv  and  5  oi  IV  in 
minor.     This  pedigree  is  3,  9,  1,  s,  5. 

6.  Fa  began  as  7  of  V  in  major,  next  appeared  as 
1  of  IV  in  major,  then  as  3  of  iv  and  ©  of  F  in  minor. 
This  harmonic  pedigree  is  7,  1,  a,  9. 

7.  Ti  began  as  3  of  V  in  major,  next  appeared  as  5 
of  V  and  5  of  v  in  minor.     This  pedigree  is  3,  5,  s. 

In  these  pedigrees  we  observe  that  of  the  nine  per- 
cepts thus  far  accounted  for  do  has  reported  three  and 
has  still  to  appear  as  1,  3,  6,  7,  9,  9;  sol  has  reported 
three  and  has  still  to  appear  as  1,  3,  s,  7,  9,  9;  mi  has 
reported  four  and  has  still  to  appear  as  s,  5,  7,  9,  9; 
re  has  reported  four  and  has  still  to  appear  as  3,  3,  s, 
9,  9;  la  has  reported  five  and  still  has  to  appear  as  1, 
8,  7,  9;  fa  has  reported  four  and  has  still  to  appear  as 
1,  3,  5,  6,  9;  ti  has  reported  three  and  has  still  to 
appear  as  1,  1,  3,  7,  9,  9.  Of  all  these  relations  still 
remaining  to  be  reported  by  diatonics  both  the  rela- 
tions and  the  harmonies  are  either  chromatic  or 
enharmonic.  The  above  pedigrees  of  seven  tones 
present  an  aggregate  of  twenty-six  harmonic  relations 
each  of  which  is  distinct  and  individual.  Thus  we 
observe  that  the  multiplication  of  harmonic  relations 
is  very  rapid  while  that  of  harmonic  percepts  is  very 
slow.  This  is  true  not  only  of  homophony,  but  of 
multi-voice  music  as  well.  Further  back  the  Zarlino- 
Riemann  theory  of  pendant  minor  was  alluded  to  as 
an  example  of  irreconcilable  conflict  between  music- 
thinking  and  music-feeling.     This  conflict  becomes 


ORIGIN  AND  NATURE  OF  MINOR  227 

evident  when  we  subject  the  foundation  of  the  theory 
to  the  test  of  harmonic  self-reports  in  one  voice,  a  test 
which  we  are  now  prepared  to  apply  having  just 
summed  up  the  original  harmonic  percepts  of  homo- 
phonic  melody  and  having  finished  our  explanations 
of  the  origins  both  of  major  and  minor.  The  theory 
in  question  is  based  on  acoustics,  and  postulates  that 
the  minor  chord  springs  from  a  descending  acoustic 
series  of  undertones  generated  by  a  root  on  the  top 
just  as  the  major  chord  springs  from  the  ascending 
acoustic  series  of  overtones  generated  by  a  root  at  the 
bottom,  that  the  minor  chord  is  the  exact  inverse  of 
the  major  chord  in  that  the  relative  intervals  and 
ratios  of  vibration  in  both  acoustic  series  are  identical, 
as  shown  below  by  the  familiar  acoustic  numbers 
1;2;3;4;5;6;8;.  Thus  at  6)  the  minor  chord  is  as 
4;  5;  6;  8;  going  down,  and  the  major  is  the  same 
going  up.     In  short,  minor  is  inverted  major. 

h) 


a) 


Minor 
Series 


Major 
Series 


5^!f^^3^ 


i= 


It  is  assumed  that  C  is  the  root  of  both  the  major 
and  minor  triads  at  6).  In  other  words,  the  sup- 
posed C-minor  triad  hangs  suspended  from  its  aerial 
root  C  just  as  the  C-major  triad  rests  upon  its  ground- 
root  C.  The  inverted  acoustic  series  forming  the 
above  minor  triad  is  a  purely  arbitrary  conception, 


228  THE  NATURE  OF  MUSIC 

since  the  existence  of  such  a  series  of  undertones  has 
never  been  demonstrated,  nor  has  it  ever  been  heard 
by  the  musical  ear.  It  cannot  be  gainsaid  that  from  a 
mathematical  point  of  view  this  hypothetical  series  of 
undertones  is  both  charming  and  fascinating,  since  to 
the  eye  its  explanation  of  the  minor  chord  appears 
both  logical  and  satisfactory.  This  probably  explains 
why  the  theory  has  won  so  many  adherents.  But  mu- 
sical hearing,  feeling  and  perception  refuse  thus  to  be 
deceived.  The  common  harmonic  self-report  of  the 
minor  triad  at  h)  is  this :  F  is  the  root,  Al?  the  third, 
C  the  fifth.  The  triad  is  F-minor,  not  C-minor.  One 
might  as  well  try  to  invert  one's  self  and  walk  on  the 
ceiling  as  try  to  perceive  C  as  the  root  of  this  triad. 
The  test  of  harmonic  self-reports  on  the  above  hypo- 
thetical minor  series  is  as  follows:  1;  or  C  =  6.  2;  or 
C=  6.  3;  or  F=  1.  4;  or  C=  «.  5;  or  A>=  s. 
6;  or  F=  i.     8;or  C=  s. 

Next  I  present  the  Zarlino-Riemann  minor  scale, 
the  tones  of  which  are  arbitrarily  conceived  as  the 
components  of  three  pendant  primary  minor  triads 
supposed  to  hang  suspended  from  the  aerial  roots  C, 
F  and  G.  Below  compare  this  pendant  minor  scale 
with  the  ascending  major  scale  and  observe  the  per- 
fect correspondence  of  the  whole  and  half  steps.  Just 
as  in  the  case  of  the  triad  so  also  here  in  the  case  of  the 
scales  the  minor  is  the  exact  inverse  of  the  major. 


-iS^ 


Majai 
Scale 


iE=E^=,=^.=^  '•       -      ±J 


ORIGIN  AND  NATURE  OF  MINOR  229 

The  test  of  harmonic  self-reports  in  one  voice  when 
applied  to  this  hypothetical  minor  scale  at  once  dis- 
closes the  fact  that  the  scale  is  major,  not  minor.  In 
whatever  rhythm  we  may  ascend  or  descend  on  this 
scale  the  resultant  melody  will  always  report  itself  as 
major,  each  individual  tone  will  report  a  major  har- 
monic percept,  in  short,  we  feel  and  perceive  in  com- 
mon that  this  scale  starts  and  ends  on  mi,  the  large 
third  of  the  major  tonic-harmony  upon  which  it  is 
based.  Our  next  example  presents  the  scale  in  its 
descending  form,  each  tone  is  named  by  a  syllable, 
each  harmonic  percept  is  marked  by  its  specific  num- 
ber. 

3     5      13     3      5^3 

mi  —  re  —  do  ^^^  ti  —  la  —  sol  —  fa  s,.^  mi 

Not  only  is  this  Zarlino-Riemann  scale  major,  but  it 
is  also  identical  with  the  ancient  Dorian  scale  of  the 
Greeks.  In  the  terms  of  our  notation  the  tonic  of 
this  scale  is  Ai?  and  not  C ;  the  basic  harmony  of  the 
scale  is  that  of  AKmajor  and  not  the  supposititious 
pendant  minor  chord  of  C. 

On  the  line  of  least  resistance,  upon  which  homo- 
phonic  harmonies  assert  themselves,  this  scale  abso- 
lutely refuses  to  report  the  minor  mode.  However, 
there  are  two  ways  in  which  in  one  voice  this  scale 
may  be  induced  to  report  itself  as  minor.  First,  by  a 
prelude  in  which  we  establish  the  feeling  of  the  minor 
consonance  as  below  at  a);  next,  by  arbitrarily  con- 
ceiving the  scale  as  minor.  In  the  first  case  the  minor 
harmonic  percepts  owing  to  the  prelude  arise  on  the 
homophonic  line  of  least  resistance,  while  in  the  second 
case  they  are  premeditated  and  therefore  selective. 


230  THE  NATURE  OF  MUSIC 

In  both  cases  the  result  as  to  harmonic  reports  is  the 
same  and  as  follows :  — 

Prelude  Scale 


^'^^^^J^^^^gd-r^'Mj^l^ 


F/. 


Now  that  we  have  transmuted  the  scale  from  major 
to  minor  thereby  demonstrating  that  it  may  report 
itself  as  minor  in  homophonic  melody  or  one  voice, 
this  question  arises :  Does  this  scale  of  minor  harmonic 
percepts  in  any  way  support  the  theory  of  pendant 
minor?  The  above  common  harmonic  self -reports 
based  on  common  harmonic  feeling  and  perception 
answer  in  the  negative.  These  self -reports  plainly 
testify  as  follows :  the  scale,  now  minor,  starts  and  ends 
on  mi  (C),  which  is  the  fifth  of  the  minor  tonic-har- 
mony based  on  la  (F) ;  its  tonic  or  point  of  complete 
repose  is  F  and  not  C;  its  tonic-harmony  is  erect 
F-minor  and  not  pendant  C-minor.  Homophonic 
harmony  and  its  common  self-reports  being  subjects 
new  to  music-theory  the  same  is  necessarily  true  of 
the  facts  here  adduced  as  well  as  of  the  conclusions  to 
which  they  point.  In  conclusion  it  remains  to  be 
said  that  besides  being  an  acoustic  theory  of  harmony 
based  on  an  acoustic  hypothesis,  the  Zarlino-Riemann 
theory  is  specifically  a  chord-theory.  Having  demon- 
strated in  preceding  chapters  of  this  book  that  chord- 
harmony  is  selective  harmony  it  is  difficult  to  see  how 
the  chord-theories  of  harmony  could  possibly  have 
escaped  the  bias  of  personal  selection  and  therefore 
of  the  personal  equation. 


ORIGIN  AND  NATURE  OF  MINOR 


231 


49.    Chords  Derived  from  the  Minor  Forms  oj  Con- 
sonance and  Dissonance  in  One  Voice 

From  the  original  minor  form  of  consonance  /  is 
derived  the  original  minor  triad  /.  All  other  minor 
triads  like  iv  and  v  are  duplicates.  Below  are  the 
triads  /,  iv,  v. 


i 


^ 


IV 


I 


Like  its  major  prototype  the  minor  form  of  disso- 
nance presents  six  chords,  namely,  the  small  ninth- 
chord  Fj,  the  two  seventh-chords  V^  and  ra°y,  the 
three  triads  F,  F77°,  77°,  as  follows:  — 


i 


7 

5       ? 
3       5 


-19- 


1 


^ 


^^^ 


<5?- 


N.B. 


vir 

7 

N.B. 


r/yc 


Jt 


Of  all  these  chords  only  two  forms  are  of  minor 
origin.  They  are  the  small  ninth-chord  Fg  and  the 
diminished  seventh-chord  F77°^,  both  marked  N.B.  in 
our  example.  Each  of  these  forms  is  the  first  of  its 
kind,  all  like  forms  being  duplicates  of  these  originals. 
The  remaining  four  chords  are  duplicates  of  forms 
which  originated  in  major  and  have  been  presented 
in  §  39.  The  first,  second  and  fourth  of  the  above 
chords  are  based  on  the  harmonic  root  mi,  the  third 


232  THE  NATURE  OF  MUSIC 

and  fifth  omit  the  harmonic  root,  the  sixth  omits 
both  the  harmonic  root  and  third.  The  superposed 
harmonic  numbers  show  that  mi  is  the  harmonic 
root  of  all  of  the  six  chords.  In  §  39  we  pointed 
out  and  explained  by  means  of  the  harmonic  self- 
reports  of  homophony  the  necessary  distinctions  be- 
tween harmonic  roots  and  chord-roots,  between  har- 
monic intervals  and  chord-intervals  and  by  the  same 
means  demonstrated  that  chords  are  often  incom- 
pletely represented  by  one  or  two  components,  some- 
times appearing  detached  from  their  harmonic  roots, 
sometimes  from  their  harmonic  roots  and  thirds,  some- 
times even  from  their  chord-roots.  These  distinctions 
and  facts  being  exemplified  in  the  above  groups  of 
chords  and  having  previously  been  explained  it  is 
enough  here  to  call  attention  to  them. 

By  comparing  the  above  minor  group  of  consonant 
and  dissonant  chords  with  the  corresponding  major 
group  in  §  39  the  reader  will  observe  that  two  chords 
identical  both  as  to  form  and  component  tones  appear 
in  both  groups.  They  are:  li  in  major  and  iv  in 
minor;  vii°  in  major  and  //°  in  minor.  Despite  their 
identity  in  form  and  component  tones  these  triads 
make  one  report  in  major  and  a  very  different  report 
in  minor,  as  shown  below. 

5      7    9         3     5     7 

1.  Major: 


2.  Minor: 


re 

—  fa- 

-la 

n 

1 

3 

5 

re- 

-fa- 

la 

ti- 

-re  — 

-fa 

VII° 

5 

7 

9 

ti- 

-re  — 

-fa 

IV  ir 


ORIGIN  AND  NATURE  OF  MINOR  233 

Obviously  this  difference  in  harmonic  report  is 
caused  by  difference  in  relation.  Just  as  in  homo- 
phony  the  self-report  of  a  specific  tone  varies  as  its 
relation  varies  just  so  in  multi-voice  music  the  self- 
reports  of  certain  specific  chords  vary  as  their  rela- 
tions vary.  No  words  can  therefore  overstate  the 
importance  of  relation,  it  is  everything.  Have  we  not 
demonstrated  in  the  genesis  and  evolution  of  harmony 
that  harmonic  form  to  relation  is  as  effect  to  cause  ? 
We  have  demonstrated  that  homophonic  melody  by 
means  of  relation  has  produced  the  original  forms  of 
harmony  and  the  original  tones  of  the  tone-system. 
Let  us  be  explicit  on  this  question  of  form  and  relation. 
The  two  are  inseparable  in  concrete  music.  So  long 
as  we  are  contemplating  and  investigating  tones  or 
chords  in  relation  so  long  only  are  we  contemplating 
and  investigating  concrete  music.  But  the  moment 
we  leave  out  relation  we  leave  out  music  and  are  then 
contemplating  and  investigating  only  the  mere  mate- 
rial of  music.  Thus  abstracted  from  relation,  a  spe- 
cific tone  is  simply  a  constituent  of  the  tone-system 
distinguishable  from  the  other  constituents  as  they 
from  it  by  relative  pitch.  A  specific  chord  thus  ab- 
stracted from  relation  is  simply  one  of  the  innumer- 
able chords  of  music's  chord-material  distinguishable 
from  other  chords  as  they  from  it  by  difference  in 
structure.  Briefly,  a  tone  or  a  chord  out  of  relation 
is  out  of  music.  The  physical,  physiological  and  psy- 
chological views,  analyses  and  theories  of  music's  raw 
material,  that  is,  of  tones  and  chords  out  of  their  dis- 
tinctively musical  relations,  have  not  discovered  a 
single  truth  about  music,  have  added  nothing  to  our 


234  THE  NATURE  OF  MUSIC 

intelligence  and  appreciation  of  music,  and  are  ut- 
terly valueless  to  music-theory  and  music-education. 
Music  itself  presents  its  own  peculiar  forms  and  rela- 
tions, in  short,  its  own  peculiar  problems  to  the  inves- 
tigator. However,  in  his  quest  for  truth  the  investi- 
gator is  in  reality  seeking  he  knows  not  what  unless 
he  equip  himself  with  the  first  essential  requisite  to 
music-research,  namely,  with  an  adequate  knowledge 
of  what  the  peculiar  forms,  relations  and  problems  of 
music  are.  After  all,  the  great  leading  question  is : 
What  is  music  ?  And  the  answer  to  this  question  has 
to  be  worked  out  independently  by  musicians.  Music 
isy  and  it  is  futile  for  physicists  to  tell  us  that  music  is 
all  wrong  and  should  be  otherwise. 

The  harmonic  reports  of  the  chords  thus  far  de- 
rived plainly  show  that  a  chord-root  may  be  a  har- 
monic root  or  third  or  fifth;  that  a  chord-third  may 
be  a  harmonic  third  or  fifth  or  seventh ;  that  a  chord- 
fifth  may  be  a  harmonic  fifth  or  seventh  or  ninth:  in 
short,  that  the  self-report  of  a  chord  is  determined  by 
its  relation  and  is  ascertained  by  harmonic  analysis 
as  here  set  forth.  No  one,  for  example,  hears  the 
component  tones  of  the  diminished  seventh-chord 
{yn^^  in  minor)  as  root,  small  third,  diminished  fifth 
and  diminished  seventh :  we  all  hear  them  as  3,  5,  7,  9. 
All  other  chords  not  based  on  harmonic  roots  furnish 
similar  examples.  Chords  are  therefore  more  than 
mere  combinations  of  tones  differing  in  structure. 
Each  component  tone  in  a  chord  reports  a  harmonic 
percept.  Therefore  correctly  defined,  a  chord  is  at 
once  a  combination  of  tones  and  a  combination  of 
harmonic  percepts,     Homophony  produced  the  origi- 


ORIGIN  AND  NATURE  OF  MINOR  235 

nal  tones  and  the  original  harmonic  percepts ;  in  poly- 
phony and  chorded  music  these  tones  and  percepts 
have  been  combined  in  well-nigh  every  conceivable 
way. 

In  parallel  examples  I  next  present  the  major  and 
minor  subtonic-seventh-chords.  Each  of  these  chords 
is  composed  of  the  four  cadence-tones  of  the  mode  in 
which  it  arose.  At  a)  the  chords  present  double 
cadences,  that  is,  simultaneously  rising  and  falling 
cadences.  At  b)  and  c)  the  cadence-tones  are  sep- 
arated and  the  cadences  become  single,  that  is,  at  b) 
they  rise,  at  c)  they  fall. 


Major 


Minor 


T=^^ — ■    ^ :?    ■    y 


i^ 


At  b)  the  bond-tones  sol  in  major  and  mi  in  minor 
combine  with  the  two  rising  cadence-tones  thus  form- 
ing the  major  and  minor  dominant-triads.  At  c)  the 
bond-tones  do  in  major  and  la  in  minor  combine  with 
the  two  falling  cadence-tones  thus  forming  the  major 
and  minor  subdominant-triads.  The  resolutions  at 
b)  present  the  authentic  ending,  at  c)  the  plagal 
ending.  The  next  example  illustrates  these  single 
cadences  and  two  endings  in  pure  diatonic  minor, 
all  the  triads  being  minor  and  composed  of  dia- 
tonics. 


236 


THE  NATURE  OF  MUSIC 


i 


f 


-s*- 


±=i^ 


p 


IV 


The  above  example  may  call  forth  this  question: 
Are  not  the  above  triads  /,  v  and  iv  identical  with  the 
secondary  triads  of  the  major  mode  known  respec- 
tively as  VI,  III  and  ii  ?  The  question  is  premature  at 
this  juncture,  but  may  be  answered  provisionally  in 
the  affirmative.  As  chords  they  are  identical  both  in 
major  and  minor,  but  their  relations  in  major  and 
minor  differ.  Their  relations  in  the  above  example 
are  in  minor,  and  each  triad  is  a  combination  of  the 
minor  harmonic  percepts  i — s — 5.  Concisely  stated, 
triads  which  are  primary  in  minor  are  secondary  in 
major  and  vice  versa. 


CHAPTER  VI 

CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN 

50.   Description  and  Summary  of  Chords  Thus  Far 

Derived 

At  present  our  list  of  triads  aggregates  five  in  major 
and  six  in  minor  as  follows :  — 


In 
Major 


fe^^^^^ 


f     II     IV    V 


VII 


In 

Minor 


iz^II^ZZ^EE^^iE^ 


11°         IV         V         V  Vjf 


This  summary  presents  only  three  distinct  types  of 
triads,  the  major,  the  minor,  the  diminished.  The 
originals  of  the  three  types  are  respectively  I  in  major, 
/  in  minor,  vii^  in  major.  All  other  triad-types  are 
either  modifications  of  the  three  originals  or  com- 
pound chords. 

The  structure  of  a  triad  is  described  when  we  name 
the  exact  interval  relations  of  its  third  and  fifth.  We 
describe  the  major  triad  as  root,  large  third,  pure 
fifth:  the  minor  triad  as  root,  small  third,  pure  fifth: 
the  diminished  triad  as  root,  small  third,  diminished 
fifth.  When  we  describe  the  structure  of  chord-types 
we  treat  each  type  as  chord-material  and  compute  the 
intervals  of  components  from  the  chord-root  without 
considering  whether  or  not  the  chord-root  is  a  har- 


238  THE  NATURE  OF  MUSIC 

monic  root.  But  in  the  harmonic  analysis  of  a  con- 
crete case  we  first  name  the  type  of  a  specific  chord 
and  then  proceed  to  describe  the  chord's  specific  rela- 
tion which  gives  us  the  harmonic  report  we  are  in 
search  of. 

There  are  three  triad-positions.  In  its  first  posi- 
tion, the  triad  is  named  the  ground-triad,  the  chord- 
root  being  its  lowest  tone.  In  its  second  position 
with  the  chord-third  as  lowest  tone,  the  triad  is  named 
the  sixth-chord  and  may  also  be  called  the  terce- 
form.  In  its  third  position  with  the  chord-fifth  as 
lowest  tone,  the  triad  is  named  the  fourth-sixth  chord 
and  may  also  be  called  the  quint-form.  The  posi- 
tions of  triads  are  further  distinguished  as  close  and 
oj>en :  close  when  the  components  are  in  closest  prox- 
imity, as  below  at  a),  o'pen  when  the  components  are 
spread  apart  as  at  6). 


a)  Close  h)  Open 


sr 


M /Q ,<3 IJ 


I  la       I|      I         la        Is 

As  everybody  knows,  all  thorough-bass  numbers 
like  6  and  |  in  our  example  indicate  intervals  as  com- 
puted from  the  lowest  tone  or  bass. 

Seventh-Chords,  We  have  thus  far  presented  four, 
two  in  major,  two  in  minor.     They  are:  — 

In  Major  In  Minor 


N.B.     N.B.  N.B. 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN      239 

This  summary  presents  three  types,  each  marked 
N.B.  Each  of  these  types  is  the  original;  the  chord- 
root  of  the  first  is  the  major  dominant,  that  of  the 
second  is  the  major  upleader,  that  of  the  third  is  the 
minor  upleader.  Every  type  of  chord  should  have  a 
name  in  terms  descriptive  of  its  structure  like  the  three 
triad-types  just  considered.  Since  any  chord-type 
may  appear  on  any  tone  in  any  key  it  would  simplify 
analysis  were  we  able  to  refer  to  each  specific  type  by 
its  structural  name  before  proceeding  to  report  on  its 
specific  relation  in  any  special  concrete  case.  The 
first  of  the  above  types  of  seventh-chords  is  known  as 
the  dominant-seventh-chord,  the  second  as  the  major 
subtonic  seventh-chord,  the  third  as  the  minor  sub- 
tonic  seventh-chord  and  also  as  the  diminished  seventh- 
chord.  All  these  names  except  the  last  are  relation- 
names.  The  first  type  is  also  known  as  the  primary 
and  also  as  the  main  (Haupt)  seventh-chord,  and  these 
names  also  describe  relation  instead  of  structure.  Be- 
fore proceeding  to  give  each  of  the  above  seventh- 
chords  its  structural  name  we  will  first  explain  how 
the  form  of  such  a  chord  is  described.  A  seventh- 
chord  is  a  combination  of  a  triad  and  a  superadded 
seventh.  Its  description  requires  two  terms,  the  first 
defining  the  triad,  the  second  defining  the  seventh. 
The  two  terms  joined  by  a  hyphen  will  give  the  exact 
structural  name  of  the  specific  type.  The  first  of  the 
three  types  (N.B.  in  our  example)  comprises  a  major 
triad  and  a  small  seventh ;  the  structural  name  of  this 
type  is  therefore  the  major-small  seventh-chord;  the 
first  of  the  hyphened  words  describes  the  triad,  the 
second  describes  the  seventh.     Accordingly  the  sec- 


240  THE  NATURE  OF  MUSIC 

ond  type  (second  N.B.  in  example)  is  named  the 
diminished-small  seventh-chord.  The  third  type  (last 
N.B.  in  example)  is  named  the  diminished-diminished 
seventh-chord,  or  briefly,  the  diminished  seventh- 
chord.  All  other  types  of  seventh-chords  are  either 
modifications  of  these  or  compound  chords. 

Next  we  exemplify  the  four  positions  or  forms  of  a 
seventh-chord.  They  are:  1.  the  ground-form  with 
chord-root  as  lowest  tone;  2.  the  terce-form  with 
chord-third  as  lowest  tone;  3.  the  quint-form  with 
chord-fifth  as  lowest  tone;  4.  the  sept-form  with 
chord-seventh  as  lowest  tone.  The  four  are  known 
respectively  as  the  ground-seventh-chord,  chord  of  the 
fifth-sixth,  chord  of  the  third-fourth,  chord  of  the  sec- 
ond.    All  appear  below  in  close  and  open  positions. 

Close  Open 

js.  -^ 

^         jsL  _         J2.        =:         ^. 


^-. — ^ ^fe' — g^      gy^ \—^. &^        ^      —^ H 


V.      V|     Vj      V,       V,      V|      V|      V, 

Ninth-Chords,  We  have  thus  far  derived  two,  the 
large  ninth-chord  in  major,  the  small  ninth-chord  in 
minor:  both  are  based  on  the  dominant,  and  each  is 
the  original  of  its  peculiar  type. 

In  Major         In  Minor 


i^^ 


V9 


The  description  of  a  ninth-chord  requires   three 
terms,  one  for  the  basic  triad,  one  for  the  superadded 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN     241 

seventh,  one  for  the  superadded  ninth.  Thus  the 
large  ninth-chord  is  described  as  major-small-large, 
the  small  ninth-chord  as  major-small-small. 

Owing  to  the  fact  that  the  chord  of  the  ninth  ex- 
tends beyond  one  octave  the  customary  inversion-idea 
cannot  be  applied  to  this  chord.  In  truth  the  idea 
though  universally  practiced  cannot  logically  apply  to 
any  chord,  since  the  inversion  of  a  chord,  like  that  of  a 
tone,  is  simply  an  impossibility.  A  triad  has  three 
positions  close  and  open,  a  seventh-chord  has  four 
positions  close  and  open,  and  each  individual  position 
is  an  individual  form  distinguished  from  other  posi- 
tions and  forms  by  its  lowest  tone  or  bass.  Thus  the 
ninth-chord  falls  in  line  with  the  triad  and  seventh- 
chord.  Having  five  components  the  ninth-chord  may 
appear  in  five  positions  close  and  open.  They  are 
presented  in  the  next  example.  The  first  position 
is  the  ground-form  with  chord-root  as  bass  and  is 
marked  ©;  the  second  with  chord-third  as  bass  is  the 
terce-form  and  is  marked  1;  the  third  with  chord- 
fifth  as  bass  is  the  quint-form,  marked  §;  the  fourth 
with  chord-seventh  as  bass  is  the  sept-form,  marked  ?; 
the  fifth  with  chord-ninth  as  bass  is  the  none-form, 
marked  9. 


or 


jO- 


^ 


or 


V9. 


242 


THE  NATURE  OF  MUSIC 


i 


-(2- 


sSzs:?: 


or   ^    or  ^ 


.^_  or        or  .a. 

"         a. 


-<s^ 


^SL 


Qr  ^    or 


9i=i^ 


-(2- 


.gi2 ^(S2- 


V?. 


vg 

The  open  positions  after  the  close  position  of  each 
of  the  above  forms  are  easily  multiplied  by  conceiving 
other  combinations  of  the  five  chord-components. 
When  viewed  as  abstract  material,  the  close  posi- 
tions of  the  above  forms  from  the  second  onward 
strike  both  ear  and  eye  as  amorphous  and  repulsive. 
But  in  the  concrete  when  each  component  reports  a 
clear  and  definite  harmonic  percept  these  chords  at 
once  gain  a  definite  shape  and  suggest  many  conjunc- 
tions with  other  chords,  some  preceding,  others  suc- 
ceeding them.  For  the  time  being  we  are  summariz- 
ing and  describing  the  structure  of  chords  the  origin 
of  which  we  have  explained  in  previous  chapters.  On 
the  other  hand,  the  treatment  of  chords  in  concrete 
music  is  the  special  subject  of  another  part  of  this 
work.  But  a  word  in  the  latter  connection  may  be 
said  here.  As  harmonies  we  have  seen  that  the  large 
and  small  ninth-chords  appear  sometimes  with  the 
root,  at  other  times  without  the  root.  With  the  har- 
monic root  the  two  above  types  are  classed  as  ninth- 
chords  ;  without  the  harmonic  root  the  resultant  chords 
are  classed  as  seventh-chords.  By  omitting  the  har- 
monic root  in  the  above  example  all  the  chords  would 
become  seventh-chords. 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN     243 

I  next  present  the  two  original  types  of  ninth- 
chords  in  a  series  of  ground-forms  very  commonly  em- 
ployed, especially  in  instrumental  music.  It  will  be 
observed  in  these  illustrations  that  while  the  chord- 
root  is  retained  throughout,  the  upper  four  tones  ap- 
pear successively  in  four  positions  first  close,  then  open. 

Large  Ninth-Chord 


l-p , 

/o                                          1 

'X 

^                                  ^       1 

-fr\   ■ 

o 

c> 

^-^ 

%])                                                  I 

ej 

e> 

if 

■f-^ 

^ 

JSL 

(or„) 

o 

^ 

c 

^^ 

^ 

^ 

— ^— 

— ^ 

f5> 

^^- 



^ 1 

— & — 

(S> — 

— <& — i 

L-^ 

& 

& — 

(S" — 

— & ■ 

V9. 


^maU.  Ninth-Chord 


^ — = 1 

— 1        ^  fr"^ 

-^-^i » 

fl^-        s^        -s>-        -s>- 

S-^      -^-      -&-      -^-     -&- 

All  other  types  of  ninth-chords  are  either  modifica- 
tions of  the  original  two  or  compound  chords. 

51.   Simple  and  Compound  Chords  Defined 

1.  A  simple  chord  is  a  combination  of  components 
of  a  single  harmony. 

2.  A  compound  chord  is  a  combination  of  compo- 
nents of  two  or  more  harmonies. 

In  the  above  summary  all  the  chords  are  simple  and 
all  the  types  there  presented  are  types  of  simple  chords. 
Their  sole  guide  having  been  harmonic  feeling  and 


244  THE  NATURE  OF  MUSIC 

perception,  the  first  builders  of  chords  worked  induc- 
tively and  were  not  troubled  by  laws  of  acoustics. 
Moritz  Hauptmann*  tells  us  that  treatises  on  harmony 
usually  open  with  a  learned  chapter  on  acoustics  the 
half-truths  in  which  have  little  if  any  influence  on  the 
chapters  that  follow.  The  truth  is  that  the  com- 
monly adopted  rules  for  building  chords  were  formu- 
lated in  accordance  with  the  dictates  of  harmonic 
feeling  and  perception.  The  rules  are:  for  building 
triads,  superadd  third  and  fifth  to  root;  for  seventh- 
chords,  superadd  seventh  to  triad;  for  ninth-chords, 
superadd  seventh  and  ninth  to  triad.  The  validity  of 
these  rules  as  applied  to  simple  chords  has  been  con- 
firmed by  the  three -tone,  four -tone  and  five -tone 
threads  of  original  harmony  in  one  voice.  This  prin- 
ciple of  chord-building  by  superadding  third  upon 
third  has  been  extended  beyond  the  ninth  to  the 
eleventh  and  thirteenth.  The  resultant  chords,  all  of 
which  are  compound,  are  known  as  chords  of  the 
eleventh  and  thirteenth.  The  above  rules  apply  ex- 
clusively to  simple  chords.  Their  application  to 
chords  in  general  is  a  purely  arbitrary  procedure  and 
has  caused  much  gratuitous  confusion  in  heads  and 
books.  For  when  our  intellectual  or  conceptual  re- 
port on  a  specific  chord  in  a  specific  relation  does  not 
agree  with  and  is  in  truth  utterly  refuted  by  our  con- 
crete perception  of  that  chord's  harmonic  report,  how 
can  we  help  feeling  confused!  Theories  that  present 
such  conceptions  are  certainly  false.  Viewed  in  the 
abstract  a  chord  is  musically  dead;  we  have  done 
with  it  when  we  describe  its  structure  and  classify  it. 
Viewed  in  the  concrete  a  chord  is  alive,  each  of  its 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN     245 


components  is  alive  with  its  harmonic  self-report,  for 
the  chord  is  musically  related.  We  are  here  con- 
cerned with  chords  that  are  alive.  We  have  seen 
that  in  concrete  music,  harmonies  may  be  completely 
and  incompletely  represented  by  chords;  completely 
when  the  chord  presents  all  the  harmonic  components, 
incompletely  when  certain  components  are  omitted. 
Whatever  their  number,  when  the  components  of  a 
chord  report  a  common  root  then  the  chord  is  simple, 
and  when  they  report  two  or  more  roots  then  the  chord 
is  compound.  The  largest  number  of  chords  in  use  are 
compound.  The  subject  of  compound  chords  belongs 
to  Part  II  of  this  work,  but  a  few  examples  at  this  junc- 
ture will  suffice  to  show  what  they  are.  To  the  two 
definitions  of  chords  at  the  opening  of  this  section  we 
now  add  a  third  which  is  general. 

3.  Chords  are  selective  combinations  of  two  or 
three  or  four  or  five  or  more  individual  tones.  They 
are  classed  under  the  following  heads :  I.  Consonant 
or  Dissonant.  II.  Simple  or  Compound.  In  the  fol- 
lowing parallel  examples  in  major  and  minor  all  the 
combinations  marked  by  asterisks,  with  the  exception 
of  the  second,  are  compound  chords.  In  these  com- 
pound biads  ^  (two-tone-chords)  the  two  tones  are 
components  of  different  harmonies;  one  reports  one 
root,  the  other  another  root. 

133     915     353135     1 
131     531     139577     3 


In 

Major 


mi: 


uiU-jMeU^ 


fVCTr-  r 


r-rrf=f 


*  The  writer  coined  the  word  biad  by  analogy  with  triad  and  tetrad.    L.  E.  K. 


246 


THE  NATUEE  OF  MUSIC 


513      133      5553391 
551      111      33317      7      7 


i 


Ui  I J  J  J  I J  j 


^ 


f 


f 


r 


r  r 


r  r 


3    3     15   3    3     3 
3    5     1      113     5 


^ 


^-J-J-fj-^L^ 


3    5    7    3     5    3 
13    3    113    1 


^dd 


Jc=^=?t 


i 


fT^TT 


CTT 


^  -X-  -X-    -Jt 

iSs  9  Ifi  SOSlsSl 


1        8 


5    3 


1       8        O        6        7 


Minor 


^^^^^^ 


ife*3 


ft^  !»rf  rr  ^n^ 


5      I     3       1    3     s 

5       5      1        a      1       X 


6        5         6        8 
8         8         8         1 


3       6       1 

7         7  7 


m 


¥=i^ii-ni 


r  r 


8        0        10        8         8  8 

8        5        1        1         1         8  6 


8         6        7        8        5         8 

1         8        3       1  1       3         1 


rri* 


^ 


Uf 


*  * 


The  above  superposed  percept-numbers,  large  and 
small,  register  our  common  perception  of  the  concrete 
harmonic  self-report  of  each  tone  in  each  biad  and 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN     247 

therefore  of  each  biad's  harmonic  relation.  Relation, 
being  the  immediate  cause  of  a  tone's  and  chord's 
specific  self-report,  is  first  of  all  a  question  of  mode: 
Is  the  mode  major  or  is  it  minor?  This  becomes 
plain  when  we  compare  the  corresponding  relations 
and  consequent  self-reports  in  these  parallel  examples. 
The  two  examples  present  a  number  of  the  same  biads, 
but  the  reader  will  observe  that  the  same  biad  makes 
one  report  in  major  and  quite  another  report  in  minor. 
In  addition  to  the  question  of  mode  one  of  three  other 
questions  enters  into  this  self-report-determining  rela- 
tion of  every  tone  or  chord.  The  three  questions  are: 
Whither.?  Whence.?  Whence  and  whither.?  The 
first  pertains  to  an  initial  tone  or  chord,  whose  self- 
reports  are  influenced  by  what  follows.  The  second 
pertains  to  a  terminal  tone  or  chord  whose  self- 
reports  are  influenced  by  what  precedes.  The  third 
pertains  to  an  intermediate  tone  or  chord  whose  self- 
reports  are  influenced  both  by  what  precedes  and 
follows.  By  concretely  thinking  and  carefully  com- 
paring these  two  examples  of  biads  the  reader  will 
appreciate  the  influences  of  this  whither,  whence 
and  whence-whither  of  relation.  One  more  remark. 
All  biads  are  incomplete  forms  either  of  triads  or 
seventh-chords  or  ninth-chords.  In  a  series  of  para- 
graphs, each  devoted  to  a  measure  of  the  above 
parallel  examples,  we  will  now  take  up  the  explana- 
tion of  the  biads  marked  by  asterisks,  first  explaining 
the  biad  in  major  and  then  the  corresponding  biad 
in  minor. 

First  Measure,     This  biad  (with  asterisk)  simul- 
taneously reports  3  of  I  and  3  of  V,  is  therefore  a 


248 


THE  NATURE  OF  MUSIC 


compound  chord  and  represents  the  major  mediant- 
triad  the  symbol  of  which  is  iii.  The  corresponding 
biad  in  minor  is  a  compound  of  a  of  /  and  3  of  F  and 
represents  the  minor  mediant-triad  known  by  the 
symbol  HJ[,  Thus  the  major  mediant-triad  is  a  com- 
pound of  the  harmonies  I  and  V:  the  minor  mediant- 
triad  is  a  compound  of  the  harmonies  I  and  V,  I  next 
present  the  full  triads  with  harmonic  report  of  each 
component. 


1.  Major  Mediant-Triad: 

3 

mi  - 
E 

5-1 

-sol- 
G 

3 

-ti 
B 

marked  III. 

2.  Minor  Mediant-Triad: 

8 

do- 

1" 

6-1 

-mi  — 
E 

3 

-  si 

marked  Hi 

The  three  tones  in  these  triads  are  known  as  the 
chord-root,  chord-third,  chord-fifth  respectively.  The 
middle  tone  (chord-third)  in  each  of  the  triads  simul- 
taneously reports  itself  as  a  component  of  two  har- 
monies. A  tone  presenting  such  a  double  report  is 
named  a  double  harmonic.  Every  compound  chord 
contains  at  least  one  double  harmonic.  Primary 
chords  are  simple :  secondary  chords,  like  those  above, 
are  compound.  Therefore  secondary  chords  are  com- 
pounds of  primary  or  simple  chords.  Before  and  after 
the  simple  chords  of  which  they  are  compounds,  the 
two  above  triads  appear  in  third-relations  and  are 
heard  as  compound  in  accordance  with  the  above 
analysis.  They  are  given  below  in  these  third-rela- 
tions and  are  marked  N.B. 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN     249 
In  Major  In  Minor 


$ 


^ 


«§- 


-(&- 


W^ 


III    I 

V     '"      V 

'  TH.   ' 

VNi 

N.B. 

N.B. 

N.B. 

N.B. 

In  short,  these  triads  are  heard  as  compound  in  all 
relations  excepting  ffth-relations,  in  which  case  they 
are  heard  as  simple  chords,  that  is,  chords  whose  com- 
ponents all  report  a  common  root.  The  structural 
description  of  the  two  triads  is  as  follows:  the  major 
mediant  (iii)  is  a  minor  triad  its  chord-intervals  being 
root,  small  third,  pure  fifth;  the  minor  mediant  (Hi) 
is  an  augmented  triad  its  chord-intervals  being  root, 
large  third,  augmented  fifth.  This  type  of  augmented 
triad  is  supposed  by  Richter  and  others  to  have  arisen 
in  minor  on  the  third  degree  of  the  scale.  This  would 
mean  that  our  example  presents  the  original  aug- 
mented chord.  We  shall  see  that  this  is  not  so,  since 
the  harmonic  percept  of  the  augmented  fifth  first 
arose  in  homophony  on  the  major  dominant,  and  we 
shall  further  see  that  the  augmented  triad  of  the 
major  dominant  is  a  simple  chord. 

Since  the  above  mediant-triads  are  compounds  of 
the  tonic  and  dominant  harmonies  of  their  respective 
modes  it  follows  that  there  are  other  secondary  triads, 
namely,  those  which  are  compounds  of  tonic  and  sub- 
dominant  and  those  which  are  compounds  of  domi- 
nant and  subdominant.  These  are  the  submediant- 
triads  vi  in  major  and  VI  in  minor,  and  the  super- 


250 


THE  NATURE  OF  MUSIC 


1.  Major: 

la- 
A 

—  do  —  mi 
C       E 

2.  Minor: 

8 

fa- 
F 

6-1         S 

—  la  —  do 
A       C 

tonic-triads  ii  in  major  and  //°  in  minor.  Thus  in 
each  mode  there  are  three  primary  and  three  secon- 
dary triads.  We  first  present  the  harmonic  analysis 
of  the  major  and  minor  submediant-triads. 

3    5-13 

VI. 


=  VI. 


It  is  only  in  certain  relations  that  these  triads  make 
the  above  self-reports.  They  do  so  when  they  appear 
as  bychords  on  light  rhythm-periods  each  before  and 
after  the  primary  triads  of  which  they  are  compounds. 
See  below:  — 

^    Major 


^m 


^ 


-Zir 


-7^ 


sr 


IV    ^i     IV 

N.B. 


VI 

NJB. 


f\ 

Minor 

-(5> 

..  1 1 

— Bj Z} — 

— 25 ■ 

^^-7^ — f— 

-*— 

— 1 i9 

V 

J     ^ 

IV 


ri       jy  I     VI        I 

N.B.  N.B. 

*  This  example  and  those  on  pp.  251  and  252,  not  found  in  the  MS.,  were 
supplied  by  Miss  Luise  Haessler.    L.  E.  K. 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN     251 

In  most  other  relations  these  secondaries  are  heard 
as  simple  chords.  Surprising  and  noteworthy  are  the 
facts  first,  that  the  triad  vi  is  at  once  a  minor  triad 
and  a  compound  of  two  primary  major  triads ;  second, 
that  the  triad  VI  is  at  once  a  major  triad  and  a  com- 
pound of  two  primary  minor  triads.  The  two  asterisk- 
biads  in  the  ninth  and  tenth  measures  of  our  parallel 
examples  represent  the  triads  in  question  and  report 
them  as  compound. 

Next  follows  the  analysis  of  the  supertonic  triads 
II  in  major  and  ii^  in  minor. 


1.  Major 


5  7-1   9-3 

re  —  fa  —  la 


D       F       A 

5     7-       «-t 

2.  Minor: 

ti  —  re  —  fa 

B       D       F 

=  n. 


IV 


These  compounds  of  V  and  IV  in  major,  V  and  IV 
in  minor,  make  the  above  self-reports  as  bychords  in 
connection  with  their  respective  modal  subdominant- 
triads  as  follows :  — 


Major 


\ 


i!^ 


¥ 


=2: 


-&- 


»  See  footnote,  p.  250. 


252 


THE  NATURE  OF  MUSIC 


Minor 


li 


9t 


IV 


3 


-#- 


7/0 

N.B. 


'K 


-&- 


-^- 


IV 


The  asterisk-biads  in  the  seventh  measure,  page 
246,  represent  these  supertonic-triads  and  are  heard 
as  compound.  Before  the  dominant  these  triads  are 
heard  as  simple  chords. 


f  Major ' 


i 


^i 


l^E& 


11         V 

N.B. 


Minor 


11 


-»■ 


^ 


-"s: 


no 
N.B. 


The  books  agree  that  this  downward  progression 
from  II  to  V  and  from  //°  to  V  is  most  natural  and 
correct,  but  do  not  satisfactorily  explain  why.     The 

*  See  footnote,  p.  250. 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN     253 

supertonic-triad  is  based  on  the  fifth  of  the  dominant 
and  therefore  lies  over  it.  Besides  this,  the  fifth  of 
the  supertonic-triad  is  the  original  ninth  of  the  domi- 
nant and  its  natural  tendency  is  downward.  Hence 
these  natural  progressions. 

Second  Measure,  The  supertonic-triads  as  simple 
chords  and  as  just  described  are  represented  by  the 
asterisk-biads  in  this  measure  which  precede  the  domi- 
nant. Their  analysis  in  this  relation  is  as  follows: 
II  =  5,  7,  9;  If  =  5,  7,  o. 

Third  Measure,  This  biad  is  a  compound  of  I 
and  V,  and  represents  the  secondary  seventh-chord  of 
the  major  mediant  11I7.  The  corresponding  biad  in 
minor,  a  compound  of  /  and  F,  represents  the  corre- 
sponding chord  7M7  in  minor.  Below  are  the  full 
harmonic  reports  on  these  chords. 

3    5-1    3     5  I 

1.  Major  :  mi  —  sol  —  ti  —  re  [  =  Illy. 

E        G       B      D  ) 

3       6-13       5  ] 

2.  Minor :  do  —  mi  —  si  —  ti  \  =  IrJJl' 

C        E      Gif     B  I 

The  remaining  secondary  seventh-chords  (except- 
ing those  of  the  major  and  minor  sub  tonics  which  we 
have  already  analyzed  and  found  to  be  simple  chords) 
are  compounds  of  primary  harmonies.  They  are 
those  of  the  two  tonics  1 7  and  1 7;  those  of  the  two  sub- 
dominants  IV7  and  iv^;  those  of  the  two  submediants 
VI7  and  VI 7;  those  of  the  two  supertonics  1I7  and  11%. 
These  chords  are  next  analyzed  in  the  order  of  their 
mention.  1 7  is  a  compound  of  the  primaries  I  and  V; 
/  7  is  a  compound  of  /  and  F,  as  follows :  — 


254. 


THE  NATURE  OF  MUSIC 


1.  Major  : 


2.  Minor 


1 

3 

5-1    3 

(fo. 

—  mi- 

-  sol  —  ti 

c 

E 

G       B 

1 

s 

6-1      3 

la  - 

-do- 

-mi  —  si 

A 

C 

E       Git 

=  17. 


z7. 


Next  follow  the  major  subdominant  seventh-chord 
which  is  a  compound  of  I  and  IV  and  the  correspond- 
ing chord  in  minor  which  is  a  compound  of  /  and  iv. 

1      3    5-13 

1;  Major  :      fa  —  la  —  do  —  mi  .  =  IV  7. 


2.  Minor 


F 

A 

C       E 

1 

8 

8-1        8 

re 

-fa- 

—  la  —  do 

D 

F 

A       C 

=  /r. 


h 

C        E 

G 

2.  Minor : 

8 

fa 
F 

6-1         8 

—  la  —  do 
A       C 

6 

—  mi 
E 

^  The  submediant  seventh-chord  in  major  is  a  com- 
pound of  IV  and  I ;  in  minor  it  is  a  compound  of  IV 
and  /,  as  follows:  — 

3    5-13     5 

1,  Major :       la  —  do  —  mi  —  sol   I  =  vi7« 


=  FI7. 


The  supertonic  seventh-chord  in  major  is  a  com- 
pound of  V  and  IV,  while  in  minor  it  is  a  compound 
of  V  and  iv^  as  follows:  — 


*  This  paragraph  omitted  in  MS.  was  supplied  by  Miss  Luise  Haess- 
ler.  L.E.K. 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN      255 


1.  Major: 


2.  Minor: 


5    7-1  9-3   5  1 

re  —  fa  —  la  —  do 
D      F       A       C 


5    ''-^ 

0-8        6 

ti  —  re  - 

-fa -la 

B      D 

F      A 

=  Ilr. 


=  IV 


While  in  certain  relations  there  are  variations  in 
the  reports  of  these  secondary  seventh-chords  they 
nevertheless  always  report  themselves  as  compound. 
These  compound  triads  and  seventh  chords  call  forth 
many  observations  which  however  belong  to  Part  II 
on  chords.  My  purpose  here  is  fulfilled  by  introduc- 
ing the  subject  of  compound  chords,  by  showing  that 
they  really  exist  and  what  they  are.  Interested  read- 
ers will  observe  the  differences  in  major  and  minor  of 
the  self-reports  of  certain  chords  which  are  identical 
in  both  modes. 

Fourth  Measure.  The  asterisk-biad  is  a  compound 
of  I  and  V  differing  from  the  compounds  thus  far  con- 
sidered. The  regnant  harmony  is  that  of  the  domi- 
nant and  is  represented  by  its  seventh  in  the  lower 
tone  and  therefore  the  upper  tone  is  a  bytone.  In 
short,  this  is  a  compound  of  regnant  tone  and  bytone, 
examples  of  which  are  very  common.  All  this  is  true 
of  the  corresponding  biad  in  minor. 

Fifth  Measure.  The  parallel  asterisk-biads  present 
similar  compounds  of  regnant  tone  and  bytone. 

Sixth  Measure.  These  compound  biads  represent 
the  major  and  minor  tonic-seventh-chords  which  we 
analyzed  a  moment  ago. 

Seventh  Measure.     These  parallel  biads  represent 


256  THE  NATURE  OF  MUSIC 

the  major  and  minor  supertonic-triads  in  relations  in 
which  they  are  heard  as  compound  chords.  They 
were  analyzed  in  the  paragraph  on  the  first  measure. 

Eighth  Measure.  Compare  this  second  biad  with 
the  last  biad  in  the  preceding  measure  and  observe 
how  the  self -report  of  a  specific  combination  may  vary 
even  in  the  same  mode.  Also  compare  the  same 
biads  in  minor. 

Ninth  and  Tenth  Measures,  Both  measures  pre- 
sent the  same  biad  in  different  positions.  This  biad 
represents  the  submediant-triad  in  a  relation  in  which 
it  reports  itself  a  compound  chord.  The  same  applies 
to  the  corresponding  biads  in  minor.  The  analysis  of 
these  submediant  triads  has  already  been  given. 

Eleventh  Measure.  These  parallel  compound  biads 
represent  respectively  the  major  and  minor  subme- 
diant-seventh-chords  which  were  analyzed  on  a  pre- 
vious page. 

Last  Measure.  Both  of  these  biads  are  based  on 
the  regnant  dominant,  and  are  therefore  compounds 
of  a  regnant  tone  and  a  bytone.  In  the  first  biad  the 
bytone  is  below,  in  the  second  it  is  above.  The  same 
is  true  of  the  corresponding  biads  in  minor.  This 
concludes  the  analysis  of  the  parallel  examples  on 
pages  245-246. 

The  only  secondary  triads  and  seventh-chords  not 
included  in  the  above  analyses  are  those  of  the  major 
and  minor  subtonics,  which  are  simple  chords,  since 
the  components  of  each  report  a  common  root.  It 
may  also  be  stated  here  that  all  secondary  ninth- 
chords  are  compounds  either  of  two  or  of  three  pri- 
mary harmonies.     In  another  chapter  we  shall  con- 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN     257 


sider  the  conclusions   to  be  drawn  from  the  facts 
adduced  from  these  analyses. 

Our  tone-material  thus  far  accounted  for  admits  of 
a  brief  presentation  of  two  other  groups  of  compound 
chord-structures  both  of  which  are  very  common  and 
have  proved  puzzling  and  difficult  to  account  for  and 
explain  by  means  of  the  arbitrary  principle  of  super- 
added thirds,  a  principle  which  in  no  way  applies  to 
them.  The  first  of  these  groups  of  chords  are  com- 
pounds of  repose-tones  and  cadence-tones,  that  is,  of 
stable  and  unstable  tones.  The  second  group  com- 
prises chords  with  superfix- tones,  infix-tones  and  sub- 
fix-tones,  that  is  to  say,  chords  with  a  tone  added 
above,  between  or  below.  Our  next  parallel  exam- 
ples present  compound  chords  of  the  first  group. 

53       5,3        353        3 
a)^      1     1      1     6)1     1       1     c)l    1        1  1 


In 
Major 


i 


^m 


T  r 


iis 


3 


* 


^ 


3 

9-3 

9-3 

,  9-3 

7-1 

7-1 

5 

5 

\    5 

5 

5 

9-3 

9-3 

1  1-5 

^)l-5 

/)l-5 

S)7-l 

/>)*-! 

258 


In 

Minor 


«) 


E 


THE  NATURE  OF  MUSIC 

h)  c) 


iS; 


1 


5 


^^S? ($'■ 


A 


-<5» -^- 


JL^^ 


All  the  above  combinations  marked  by  asterisks  are 
compounds  either  of  the  two  primaries  I — V  in  major 
and  / — V  in  minor,  or  of  the  three  primaries  I — V — IV 
in  major  and  / — V — iv  in  minor. 

The  chords  in  a),  6),  c),  d),  e)  and  /)  are  com- 
pounds of  one  stable  tone  plus  one,  two,  three  and 
four  unstable  tones  respectively.  The  stable  tone 
do  \  (C)  is  the  chord-root  of  each  of  these  compound 
chords.  Why?  First,  because  being  the  tone  to 
which  the  other  tones  are  added  and  being  stable  it  is 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    259 

the  principal  tone  in  each  chord ;  second,  because  it  is 
the  harmonic  root  of  the  chord  into  which  each  of 
these  compound  chords  resolves.  The  chords  in  g) 
and  h)  are  compounds  of  two  stable  tones  plus  three 
and  four  unstable  tones  respectively.  Both  of  these 
stable  tones  do  (C)  and  sol  (G)  are  harmonic  roots,  but 
for  the  reasons  just  given  do  (C)  is  the  chord-root  of 
these  compounds.  The  harmonic  root /a  (F)  which 
appears  in  these  chords  is  in  every  case  an  unstable 
tone.  The  chord-root  of  these  compounds  may 
appear  below,  between  or  above  the  other  chord- 
components,  but  the  ground-form  or  fundamental  posi- 
tion of  these  and  like  chords  is  that  form  or  position 
in  which  the  chord-root  is  lowest  tone  or  bass.  In  all 
cases  the  structure  of  these  chords  is  described  in 
accordance  with  the  ground-form  and  in  the  inter- 
val-terminology of  thorough  bass.  On  the  other 
hand,  the  harmonic  reports  of  these  chords  are  deter- 
mined by  the  concrete  relations  in  which  they  appear. 
While  this  species  of  compound  chord  may  arise  on 
any  tone  their  occurrence  is  most  frequent  on  the 
major  and  minor  tonics  and  dominants.  There  are 
so  many  types  of  this  species  of  chord  that  we  now 
present  only  a  few  others  and  defer  their  harmonic 
analysis  owing  to  the  fact  that  they  introduce  har- 
monic percepts  not  yet  accounted  for. 


i»^^^=^ 


jS^ 


CA-i <g^v.^<« g2>x^ 


:^ 


260 


THE  NATURE  OF  MUSIC 


jC«==- 


(2-^ — L, , ^_ gy-,_ «22J==» (2. 


The  above  ties  for  stable  tones,  and  cadence-marks 
for  unstable  tones  plainly  indicate  the  resolutions  of 
these  compound  chords  into  the  major  tonic-harmony. 
To  the  eye  the  first  three  chords  appear  to  be  nothing 
but  fourth  positions  of  the  diminished  seventh-chord 
based  on  the  chord-root  Djj!  in  which  case  the  chords 
would  be  simple.  Not  so  to  the  ear.  In  all  these 
chords  do  (C)  is  stable  and  reports  itself  as  harmonic 
root,  that  is,  as  1.  The  attempt  to  think  do  in  these 
compounds  as  a  small  ninth  and  as  unstable,  in  short, 
as  anything  but  1  and  stable,  results  in  a  voluntary 
intellectual  strain  which  is  wholly  unsupported  and 
contradicted  by  the  common  reports  of  feeling  and 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    261 

perception.  As  to  number  and  variety  there  is  no 
limit  to  compound  chord-structures  of  this  group,  since 
they  include  every  imaginable  combination  of  one  or 
two  or  three  stable  tones  plus  from  one  to  four  dis- 
tinct unstable  tones  in  forms  in  which  each  compound 
tone  appears  but  once  and  in  other  forms  in  which 
components  are  doubled  and  even  trebled.  More- 
over, these  compound  chords  may  be  conceived  on  any 
tone  and  in  endless  relations.  In  fine,  these  chords 
are  distinct  structures  because  each  may  be  a  regnant 
harmony  in  which  relation  the  components  of  each 
are  regnant  tones.  The  fact  that  as  regnant  har- 
monies each  of  these  compound  chords  may  be  elab- 
orated with  its  bytones  may  prove  suggestive  to  com- 
posers in  that  it  points  to  a  wealth  of  new  melodic, 
harmonic  and  polyphonic  possibilities  as  well  as  to 
many  as  yet  unthought  and  unpenned  ornamental 
figures  and  passages.  The  study  and  elaboration  of 
these  compound  chords  as  well  as  of  others  about  to 
be  presented  may  serve  as  a  stimulus  to  the  com- 
poser's thought  and  imagination. 

Attention  is  next  directed  to  what  on  a  previous 
page  was  called  a  second  group  of  compound  chords. 
The  description  of  these  chords  is  roughly  as  follows : 
Each  of  these  structures  has  a  triad  for  its  nucleus  and 
to  this  triad  one  tone  is  added  either  above  or  below. 
The  tone  when  added  above  is  a  supersixth  of  the 
chord-root  and  the  resultant  combination  is  named  a 
swpersixth-ohord.  The  tone  when  added  below  is  a 
subsecond  of  the  chord-root  and  the  resultant  chord 
is  named  a  suhsecond-ohord.  To  understand  these  or 
any  other  chords  they  must  be  conceived  in  the  con- 


262  THE  NATURE  OF  MUSIC 

Crete  as  regnant  harmonies  the  self-reports  of  which 
are  perfectly  distinct.  The  distinctive  peculiarity  of 
these  compounds  is  simply  this :  The  added  tone  does 
not  disturb  the  identity  and  "predominance  of  the  triad. 
Conversely,  the  triad  preserves  its  identity,  regnancy 
and  predominance  after  the  tone  is  added.  For  ex- 
ample :  after  superadding  A  to  the  C-major  tonic-triad 
the  triad  still  retains  its  identity,  regnancy  and  pre- 
dominance and  we  hear  the  new  combination  as  the 
major  tonic-triad  plus  the  added  tone.  True,  the 
resultant  chord  is  a  new  and  distinct  idea  and  unity, 
and  the  added  tone  adds  something  new  to  the  self- 
reports  of  the  triad-components,  thus  creating  the 
compound  chord,  nevertheless  the  truth  of  our  thesis 
persists,  the  triad  does  not  lose  its  identity  and  pre- 
dominance. The  nucleus-triad  of  a  supersixth  or  sub- 
second  chord  may  be  major  or  minor  or  augmented 
or  diminished,  and  every  type  of  these  chords  may  be 
found  on  any  tone  in  any  key.  This  conveys  some 
idea  of  their  limitless  number.  Below  in  parallel  ex- 
amples are  supersixth-chords  based  on  the  triads  of 
the  major  and  minor  tonics,  dominants  and  subdomi- 
nants  in  a),  h)  and  c)  respectively.  These  chords 
are  marked  by  adding  the  symbols  +6  to  the  bass- 
number,  pitch-modifying  signs  being  added  when 
necessary. 


In    6^'     ^       ^ 
Major 


l^    Y       Y    Y^ii     Y     IV  IV+e  I 
*  *  * 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    263 


Minor 


f 


While  the  added  tone  in  each  above  supersixth- 
chord  does  not  disturb  the  identity  and  regnaney  of 
the  nucleus-triad  it  does  affect  the  two  lower  tones  of 
the  nucleus-triad  in  that  it  transmutes  them  from 
simple  to  compound  harmonics.  In  fact,  the  added 
tone  and  these  two  lower  tones  of  the  nucleus-triad 
combine  in  and  represent  another,  a  second  triad  in 
each  such  chord.  Hence  this  definition:  A  super- 
sixth-chord  is  a  complex  of  two  triads  one  of  which  pre- 
dominates and  is  the  nucleus.  How  do  we  know  which 
of  the  two  triads  is  the  nucleus  ?  This  is  reported  by 
the  regnant  harmony.  We  will  analyze  the  first  of 
these  chords  marked  I  4-6  in  a).  This  chord  is  a 
complex  of  I  (C-major  triad)  and  vi  (A-minor  triad). 
Of  these  two  triads  the  former  is  at  once  nucleus, 
tonic,  primary  and  simple,  while  the  latter  is  at  once 
submediant,  secondary  and  compound,  a  compound  as 
already  shown  of  the  harmonies  I  and  IV.  Thus 
I  +  6  is  a  complex  of  the  triads  I — vi  and  a  compound 
of  the  harmonies  I — IV.  A  compound  chord  how- 
ever complex  is  a  distinct  idea  and  unit;  it  differs 
from  every  other  chord  of  the  same  and  other  species 
though  its  structure  may  be  similar;  it  is  felt,  heard 
and  thought  as  a  single  idea,  which  is  the  direct  pro- 
duct of  its  specific  combination.  This  will  appear  as 
we  proceed  to  analyze  the  other  supersixth-chords  of 
our  example.     In  a)  the  chord  /  +  6  is  a  complex  of 


264  THE  NATURE  OF  MUSIC 

the  triads  I — VI  and  a  compound  of  the  harmonies 
7 — IV,  In  h)  V  +  6  (major)  is  a  complex  of  the 
triads  V — iii  and  a  compound  of  the  harmonies  V — I, 
while  F  +  6  (minor)  is  a  complex  of  the  triads  V — TH 
and  a  compound  of  the  harmonies  V — I.  In  c) 
IV  4-  6  (major)  is  a  complex  of  the  triads  IV — ii  and 
a  compound  of  the  harmonies  IV — V  against  which 
IF  +  6  (minor)  is  a  complex  of  the  triads  iv — n^  and 
a  compound  of  the  harmonies  iv — V.  Our  analysis 
suffices  to  show  the  exact  structure  of  these  chords  and 
suggests  their  natural  relations  to  other  chords  which 
we  shall  consider  in  Part  II. 

Rameau  first  conceived  and  presented  the  super- 
sixth-chord  which  he  found  on  the  major  subdomi- 
nant-triad  (as  above  in  c))  and  of  which  he  explained 
that  the  added  tone  did  not  change  the  triad.  But  all 
the  other  supersixth-chords  in  our  example  are  formed 
in  the  same  way,  are  for  the  most  part  in  the  same 
common  use,  are  equally  distinct  ideas,  the  harmonic 
report  of  each  being  equally  distinct  and  definite;  in 
short,  they  are  actualities  not  to  be  overlooked  and 
commanding  general  recognition. 

The  fact  that  each  of  the  above  chords  is  a  complex 
of  two  triads  in  which  one  of  the  two  triads  is  nucleus 
and  predominates,  naturally  suggests  this  question: 
Does  the  other  triad  in  each  of  these  complexes  ever 
assert  itself  as  nucleus  and  ^predominant  ?  Yes,  it  does. 
By  what  test  is  this  to  be  verified  and  known  .^  By 
the  immutable  report  of  regnant  harmony.  All  this 
is  conclusively  demonstrated  in  the  next  group  of 
parallel  examples  in  which  the  asterisked  chords  fol- 
low each  other  in  the  same  order  as  those  in  the  pre- 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    265 


ceding  group  of  examples.  One  by  one  in  their  given 
order  let  the  reader  compare  the  corresponding  aster- 
isk-chords in  both  groups  of  examples.  He  will  ob- 
serve that  each  of  the  corresponding  chords  in  both 
groups  is  a  combination  of  the  savie  tones,  a  complex 
of  the  same  triads,  a  compound  of  the  sayne  harmonies. 
But  nevertheless  each  chord  in  the  group  of  examples 
below  is  an  entirely  different,  new  and  distinct  struc- 
ture  and  idea.  The  structure  is  as  follows.  Each  of 
the  asterisked  chords  below  is  formed  by  subadding  a 
second  to  a  triad  and  is  named  a  subsecond-chord. 
The  symbols  +  2  mark  the  subsecond-chord. 


In 
Majoi 


a) 


b) 


-g>  £/^ 


VI 


vi+a 


a) 


In 

Minor 


-i   2 


-aag 


IV 


J2. 


^^ 


kh^ 


t 


c) 


25^- 


is: 


3 


^z^ 


I     I 


-i&f2 


I 


111+3       T 


II 


II+3 
* 


V. 


i 


0) 


li=i 


VI    F7+a  '""      "^  f- 


^_^;^=g_^ 


I 


JJ9  IJO+2  Vrj 


The  concrete  idea  of  each  of  the  above  subsecond- 
chords  is  explained  in  the  terms  of  harmonic  analysis 
as  follows:  In  a)  the  chord  vi  +  2  (major)  is  a 
complex  of  the  two  triads  vi — I,  vi  predominating, 
and  a  compound  of  the  harmonies  I — IV:  against  this 
F/  +  2  (minor)  is  a  complex  of  the  triads  VI — /,  VI 
predominating,  and  a  compound  of  the  harmonies 
/ — IV.  In  b)  III +  2  is  a  complex  of  the  triads 
III — V,  III  predominating,  and  a  compound  of  the 


266 


THE  NATURE  OF  MUSIC 


harmonies  I — ^V,  against  which  TH  +  2  (minor)  is  a 
complex  of  the  triads  KZ — F,  TH  predominating,  and 
a  compound  of  the  harmonies  / — F.  In  c)  the  chord 
II +  2  (major)  is  a  complex  of  the  triads  ii — IV,  ii 
predominating,  and  a  compound  of  the  harmonies 
V — IV,  against  which  //°  +  2  (minor)  is  a  complex  of 
the  triads  ll° — iv,  ii^  predominating,  and  a  compound 
of  the  harmonies  F — iv. 

Analysts  do  not  agree  on  the  chord  in  the  opening 
measures  of  Beethoven's  Sonata  Op.  31  No.  3.  This 
chord  is  ii  +  2  in  its  5  position,  the  one  above  in  c), 
as  shown  in  our  next  illustration.  Most  of  these 
chords  appear  both  in  major  and  minor,  their  har- 
monic reports  varying  as  their  relations  are  changed. 
Thus,  for  example,  the  chord  vi  +  2  (above  in  major) 
appears  in  minor  where  it  becomes  /  +  2.  This  is 
exemplified  below  in  the  opening  measures  of  Bee- 
thoven's Sonata  Op.  27  No.  2. 

Op.  31.     No.  S. 


i^ 


i^ 


-m 


i^ 


e 


r 


f 


n+2- 


zg:      zg:     ::gi 


Op.  27.     No.  2. 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    267 


The  thorough-bass  mark  of  the  ground-form  or 
first  position  of  a  supersixth-chord  is  5,  of  that  of  a 
subsecond-chord  is  2.  These  chords  being  combina- 
tions of  four  tones  naturally  have  four  positions  both 
in  close  and  open  voicing.  Since  a  combination  of 
the  same  four  tones  is  now  a  supersixth-chord  and  now 
a  subsecond-chord,  now  reports  itself  in  major,  now 
in  minor,  since  each  such  chord  may  appear  in  one  of 
four  positions  either  in  close  or  open  voicing,  how  is 
it  possible  to  tell  which  is  which?  Always  by  the 
report  of  regnant  harmony,  which  is  absolute.  The 
chords  1  +  6  in  major  and  /-f2  in  minor  are  com- 
binations of  the  same  four  tones  and  will  serve  to  illus- 
trate all  these  points.     Both  are  presented  below, 

a)     In  Major  h)     In  Minor 

5    3  1 


Close 


Open 


268  THE  NATURE  OF  MUSIC 

each   in   four   positions   in   close   and   open  voicing 
together  with  its  pecuKar  thorough  bass  numbers. 

In  a)  the  regnant  harmony  of  melody  and  chord 
report  the  major-tonic-triad  as  nucleus  and  predomi- 
nant, C  (do)  as  chord-root  and  A  (la)  as  added  tone. 
In  b)  the  same  sources  report  the  minor  tonic-triad 
as  nucleus  and  predominant,  A  (la)  as  chord-root, 
G  (sol)  as  added  tone.  To  the  eye  the  chords  in  a) 
and  b)  appear  to  present  the  same  structures  and 
ideas:  to  the  ear,  as  the  above  analysis  shows,  they 
present  entirely  distinct  structures  and  ideas.  In  a) 
we  all  hear  a  major  triad  plus  a  supersixth ;  in  b)  we 
all  hear  a  minor  triad  plus  a  subsecond.  If  music  is 
what  we  hear  rather  than  what  we  see  then  supersixth- 
chords  and  subsecond-chords  are  positive  realities 
and  facts  of  common  concrete  experience  which  are 
recorded  in  every  music-score  and  confirmed  in  every 
musical  mind.  But,  it  will  be  asked,  are  not  the 
above  chords  as  well  as  all  the  other  supersixth  and 
subsecond  chords  thus  far  presented  simply  secondary 
seventh-chords  ?  Yes  and  no.  Yes,  in  the  sense  that 
they  are  commonly  known  and  classed  as  such.  Em- 
phatically 710,  in  the  sense  that  their  structure  is  the 
same  as  that  of  the  actual  harmonic  seventh-chords 
V7  in  major  and  V^  in  minor.  Once  more,  closely 
observe  the  above  two  chords  1  +  6  and  7  +  2.  Does 
either  of  the  two  contain  a  harmonic  seventh  ?  No : 
in  certain  positions  both  chords  present  a  seventh,  but 
this  seventh  is  a  c/torc^-seventh,  that  is,  an  arbitrary 
thorough-bass  seventh  computed  from  an  arbitrary 
chord-root;  it  is  not  a  harmonic  seventh,  as  the  fol- 
lowing analysis  proves.     Above  in  a)  the  chord  1  +  6 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN 

reports  the  components  of  its  nucleus-triad  to  be  1,  3,  5 
of  I  and  reports  its  added  tone  to  be  3  of  IV,  while  in 
b)  the  chord  /  +  2  reports  the  components  of  its 
nucleus-triad  to  be  i,  3,  s  of  /  and  reports  its  added 
tone  to  be  5  of  ///.  Thus  neither  of  the  two  chords 
contains  and  reports  a  harmonic  seventh.  Hence  this 
obvious  question:  Should  chords  without  harmonic 
sevenths  be  known  and  classed  as  seventh-chords? 
Thorough-bass  answers  yes;  harmony  answers  no. 
That  is  to  say,  from  the  view-point  of  thorough-bass 
the  above  chords  are  seventh-chords,  from  the  view- 
point of  harmony  they  are  not.  If  we  distinguish 
between  the  two  view-points,  both  of  which  are  neces- 
sary, there  need  be  no  difficulty  or  confusion.  In  fact, 
the  prevalent  thorough-bass  system  and  its  termi- 
nology are  indispensable  to  the  theory  and  practice  of 
harmony;  not  only  is  their  utility  unquestionable,  but 
they  have  become  fixed  habits.  The  adoption  of  a 
simple  and  exact  term  from  the  German  will,  I  think, 
remove  the  whole  difficulty.  To  explain:  For  triad 
the  German  says  Dreiklang,  for  seventh-chord  the 
German  says  not  only  Septimenaccord,  but  also  Vier- 
klang.  Vierklang  is  the  term  in  question.  According 
as  we  may  prefer  its  Latin  or  Greek  derivation  the 
English  equivalent  of  Vierklang  is  quadrad  or  tetrad. 
I  suggest  the  adoption  of  the  term  tetrad  as  the  class- 
name  of  all  chords  of  four  components.  Tetrads  may 
be  subdivided  into  as  many  distinct  groups  as  there 
are  distinct  structures.  Thus  seventh-chords  would 
form  one  group,  supersixth-chords  would  form  another 
group,  subsecond-chords  still  another,  and  so  on. 
Such  a  classification  would  not  only  conform  both 


270 


THE  NATURE  OF  MUSIC 


with  harmony  and  thorough-bass  and  render  the  two 
reciprocally  explanatory,  but  it  would  enable  us  to 
say  truly  that  certain  tetrads  are  seventh-chords, 
certain  other  tetrads  are  supersixth-chords,  and  so 
forth.  This  would  deliver  us  from  that  unnecessary 
and  harassing  evil  of  trying  to  force  all  chords  to  fit 
into  one  of  a  few  arbitrary  and  conventional  thorough- 
bass patterns.  The  truth  is  that  music  resembles 
nature  in  that  its  species  and  varieties  of  distinct  struc- 
tures are  countless  and  limitless.  Everywhere  in 
nature  there  is  music,  everywhere  in  music  there  is 
nature. 

In  the  next  parallel  examples  the  same  four  tones 
combine  in  forming  a  subsecond-chord  in  a)  and  a 
supersixth-chord  in  6).  The  subsecond-chord  in  c) 
and  the  supersixth-chord  in  d)  are  likewise  combi- 
nations of  the  same  four  tones.  These  chords  are 
marked  by  asterisks  and  their  forms  are  explained  by 
the  accompanying  symbols.  Minuter  analysis  is  un- 
necessary here  since  each  chord  is  a  complex  of  triads 
and  compound  of  harmonies  similar  to  those  previ- 
ously presented  and  analyzed. 


a) 


Major 


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CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    271 


In 

Minor 


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In  the  chords  marked  by  asterisks  the  next  collec- 
tion of  parallel  examples  presents  supersixth-chords 
in  each  of  which  the  added  tone  is  either  a  chromatic 
or  an  enharmonic.  Most  of  these  chords  are  familiar 
and  are  known  in  current  text-books  by  other  names. 
In  structure  and  idea  they  present  and  report  them- 
selves as  tetrads  of  the  supersixth-group,  of  which 
there  are  as  many  varieties  as  there  are  distinct  struc- 
tures. The  possible  connections  of  these  chords  being 
wellnigh  boundless  only  a  few  examples  are  given,  and 
owing  to  the  fact  that  we  have  not  yet  explained  the 
genesis  of  these  chromatic  and  enharmonic  harmonies 
which  these  chords  represent,  their  further  analysis  is 
deferred. 


In 

Major 


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272 


THE  NATURE  OF  MUSIC 


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The  compound  tetrad  having  been  introduced  and 
explained,  the  subject  is  here  dropped.  Of  several 
other  distinct  species  of  compound  chords  I  will  point 
out  but  one  more  with  which  the  present  provisional 
exposition  of  this  wide  and  fertile  jfield  of  inquiry  may 
be  brought  to  a  conclusion.  The  harmonic  analysis 
of  the  peculiar  and  distinct  chord-structures  now  con- 
fronting us  and  marked  by  asterisks  in  the  next  group 
of  examples  is  omitted  save  in  one  important  particu- 
lar, namely:  the  harmonic  root  of  each  such  chord  is 
indicated  by  a  capital  letter.  Thus  the  harmonic 
root  of  the  asterisked  chords  in  a)  is  G,  in  6)  is  C, 
and  so  on.  The  key  being  C  major  the  harmonic 
root  G  in  a)  is  the  dominant,  C  in  6)  is  the  tonic,  and 
so  on.  These  harmonic  roots  are  reported  by  the 
regnant  harmony  in  each  instance. 


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CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    273 
3.  6)1.  2. 


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274 


THE  NATURE  OF  MUSIC 
2.  3. 


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Each  of  these  chords  is  a  regnant  harmony,  each 
component  of  each  chord  is  therefore  a  regnant  tone 
and  reports  a  harmonic  percept.  For  the  present  this 
ends  our  harmonic  analysis  of  these  structures  because 
each  reports  certain  harmonic  percepts  which  will  not 
be  explained  and  ascertained  until  we  reach  the  chapter 
on  chromatic  and  enharmonic  harmony.  Our  present 
description  of  these  chords  will  therefore  be  superficial 
because  confined  to  the  abstract  interval-terms  of 
thorough-bass  but  will  nevertheless  suffice  for  their 
introduction.  The  peculiarity  common  to  all  these 
compound  chords  and  rendering  them  distinct  from 
all  others  is  this:  Each  contains  two  distinct  com- 
ponents answering  at  once  to  the  same  letter-name  and 
to  the  same  interval-denomination  as  chord-root, 
chord-third  and  so  forth.  Observe  the  asterisked 
chord  in  a)  1  and  2 :  it  contains  a  G  and  a  G^:  G  is  the 
chord-root,  Gjj!  is  the  chord-root  sharped:  apparently 
the  chord  has  two  roots:  harmonically  of  course  this 
is  not  the  case :  regnant  harmony  reports  that  G  is  the 
chord-root  and  that  Gjt  is  an  added  tone.  The  aster- 
isked chord  in  h)  1  and  2  contains  Eb  and  Ejj!,  that 
in  3  contains  E  and  E^:  thus  each  of  these  chords 
contains  two  distinct  chord-thirds  of  the  root  C.     The 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    275 

asterisked  chord  in  c)  1  and  2  contains  Gi?  and  Gj^, 
that  in  3  contains  G  and  Gi?,  that  in  4  contains  A 
and  Ati:  each  contains  two  distinct  chord-fifths  of  a 
common  chord-root.  Likewise  each  of  the  asterisked 
chords  in  d)  contains  two  distinct  chord-sevenths  of 
the  same  root,  in  ^)  two  distinct  chord-ninths  of  the 
same  root.  Now  it  may  be  objected  that  all  these 
structures  are  nothing  but  passing  chords.  Yes,  but 
they  are  chords  all  the  same,  each  is  regnant,  each  is 
a  combination  of  harmonic  percepts  and  subject  to 
harmonic  analysis.  Next  it  may  be  objected  that  the 
above  notation  of  these  chords  is  arbitrary  and  incor- 
rect, that  in  the  asterisked  chord  in  a),  for  example, 
we  might  substitute  At?  for  G^  and  then  the  chord 
would  simply  be  the  small  ninth-chord  of  the  domi- 
nant, marked  V^.  I  reply  that  Ab  in  this  chord  would 
be  absolutely  false  and  misleading  for  two  patent 
reasons.  First,  because  A]7  is  a  chromatic  down- 
leader  with  a  downward  tend  whereas  the  regnant 
harmony  reports  a  chromatic  upleader  with  an  uptend  : 
hence  G^.  Second,  because  the  step  from  AU  in  this 
chord  to  Ajl  in  the  next  chord  reports  a  progression 
whereas  the  relative  and  regnant  harmony  report  this 
specific  step  to  be  a  rising  cadence  and  resolution :  hence 
again,  Gjji.  On  its  logical  side  no  one  will  gainsay  that 
the  symbols  of  notation  to  be  accurate  should  be 
selected  in  conformity  with  the  harmonic  idea  to  be 
conveyed,  and  that  this  should  be  insisted  on  even  at 
the  cost  of  certain  old  and  time-honored  traditions 
and  conventions,  the  preservation  of  which  is  the  func- 
tion of  history  but  whose  usefulness  in  practice  no 
longer  exists.     Certainly  our  20th-century  notation  of 


276 


THE  NATURE  OF  MUSIC 


the  classics  should  discard  the  many  inaccuracies  of 
the  17th-  and  18th-century  notation.  At  best  our 
notation  has  its  limitations;  still  its  symbols  are 
adequate  for  a  more  accurate  presentation  of  the  har- 
monic idea.  Editors  have  done  much  in  this  direc- 
tion, but  editions  still  contain  many  harmonic  errors. 
How  are  these  errors  discovered.?  By  the  common 
immutable  self-reports  of  regnant  harmony.  Correct 
harmonic  notation  is  a  question  of  conformity  with 
these  common  self -reports.  I  will  stop  here  for  but 
one  illustration  and  quote  the  subjoined  measure  from 
the  Adagio-theme  of  Beethoven's  E  flat  piano-con- 
certo, the  error  in  which  was  corrected  by  von  Biilow 
in  the  Cotta-edition,  but  still  occurs  in  other  editions. 
At  N.B.  in  a)  the  melody  distinctly  and  unmistakably 
reports  itself  as  the  large  third  of  Djjl,  that  is,  as  F  X  : 
see  correction  at  N.B.  in  b).  Instead  of  F  X  Bee- 
thoven wrote  Gij,  which  is  a  diminished  fourth,  and  Gjj 
reappears  in  every  repetition  of  the  melody  throughout 
the  Adagio:  see  in  Peters'  edition.  It  is  impossible 
to  hear  this  specific  tone  in  this  specific  relation  as  a 
diminished  fourth,  nor  could  Beethoven  so  have  heard 
or  conceived  it.  The  common  self-report  as  large 
third  is  immutable  and  therefore  the  notation  Gtf  is 
misleading  and  false  while  that  of  F  X  is  logical  and 


a) 


M 


b) 


^ 


6E^ 


t=w. 


N.B. 


N.B. 


§S& 


P^ 


^^? 


^ 


— I 1 «- 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    277 

true.  To  the  speller  and  performer  of  notes  such 
errors  are  not  troublesome:  it  is  otherwise  with  the 
reader  and  interpreter  of  ideas, 

52.  Melody  the  Original  Reporter  of  Harmony,  There- 
fore the  Natural  Preceptor  and  Guide  in  the  First 
Studies  in  Chords 

The  thread  of  this  exposition  is  here  temporarily 
dropped  in  order  to  inquire  into  the  most  simple  and 
direct  way  of  insuring  from  the  outset  the  student's 
musical  understanding  and  mastery  of  the  chord- 
material  taken  up  from  lesson  to  lesson.  The  ground- 
forms  of  the  three  primary  triads  I,  V,  IV  constitute 
the  material  of  the  usual  first  lesson.  It  is  customary, 
after  explaining  this  material  and  giving  rules  for  its 
treatment,  to  embody  it  in  a  group  of  exercises  each 
consisting  in  a  series  of  fundamental  basses.  The 
student  then  fills  in  the  chords,  in  doing  which  he 
carefully  ties  the  bond-tones  and  avoids  the  imper- 
missible consecutive  fifths  and  octaves.  This  lesson 
is  followed  by  others,  each  adding  more  material, 
more  rules  plus  exceptions  to  or  modifications  of  pre- 
vious rules,  more  exercises  in  the  bass,  more  per- 
formances by  the  student,  and  so  the  work  proceeds. 
It  is  well  known  that  in  performing  these  tasks  most 
students  do  not  exercise  their  natural  musical  facul- 
ties in  the  slightest  degree,  they  see  but  do  not  hear 
what  they  write,  their  observance  of  rules,  their  per- 
formances are  purely  mechanical.  Such  unprofitable 
results  point  directly  to  some  radical  defect  in  teach- 
ing, to  some  psychological  error  in  our  pedagogy. 


«78  THE  NATURE  OF  MUSIC 

How  account  for  this  defect,  what  is  its  cause  ?  The 
majority  of  those  composing  the  rank  and  file  of  stu- 
dents are  only  moderately  endowed  with  musical  gifts, 
yet  each  student  sets  out  with  a  deep  love  of  music  and 
that  love  is  the  certain  proof  that  he  possesses  innate 
musical  faculties,  the  activity  and  healthy  growth  of 
which  it  is  the  function  of  eflBcient  pedagogy  to  stim- 
ulate and  direct.  The  defect,  its  cause,  indeed  the 
source  of  the  whole  difficulty  lie  in  the  universally 
adopted  form  in  which  the  work  is  presented  to  the 
student,  namely,  in  the  exercises  in  fundamental 
basses,  in  short,  in  the  fundamental  basses.  To  be 
sure,  the  fundamental  tone  is  the  only  true  viewpoint 
of  chord-material  as  such  in  the  light  of  its  structure, 
since  each  structure  Tests  and  is  built  upon  its  root  or 
fundamrental.  This  being  true  it  would  seem  that  the 
only  natural  and  logical  form  of  first  exercises  for 
students  is  that  of  a  series  of  fundamentals  as  is  the 
prevailing  custom.  So  it  would  seem,  but  it  is  not 
true.  Our  pedagogy  has  failed  adequately  to  dis- 
criminate between  two  essentially  distinct  viewpoints 
of  chord-material;  first,  that  of  the  chord  as  a  struc- 
ture and  mere  material;  second,  that  of  the  chord  as 
applied  in  the  living  stream  of  connected  rhythmo- 
harmonic  feeling  and  thought.  The  first  of  these 
viewpoints  is  that  of  the  fundamental  tone.  The  sec- 
ond, as  the  above  heading  and  all  thus  far  said  in 
these  pages  imply,  is  melody.  Melody  is  the  stu- 
dent's first  consciousness  of  music,  in  melody  he  rec- 
ognizes both  the  object  and  the  proximate  cause  of  his 
love  of  music,  to  him  melody  is  from  the  outset  some- 
thing real,  tangible,  comprehensible,  the  one  thing  he 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    279 

feels,  can  follow  and  express  because  of  his  innate 
sense  of  the  relations  of  its  tones  and  of  the  natural 
form  and  sequence  of  its  phrases,  the  one  thing  he 
knows  and  delights  in,  the  one  thing  which  to  him  is 
music.  From  all  this  the  student  is  cut  off  by  an 
exercise  in  fundamentals  at  the  sight  of  which  his 
musical  faculties  not  being  stirred  are  as  dead.  The 
student's  intellectual  grasp  of  the  rhythmo-harmonic 
form  and  content  of  a  simple  melody  should  be  the 
first  end  and  aim  of  a  teacher.  How  this  is  done  has 
been  shown  in  preceding  chapters.  Tell  him  that 
each  tone  in  melody  conveys  two  definite  and  simul- 
taneous reports  to  his  perceptions,  a  rhythmic  report 
and  a  harmonic  report.  Associate  these  reports  with 
correct  symbols  and  the  student's  feeling  and  thought 
are  connected  for  all  time.  The  resultant  intellectual 
grasp  of  these  reports  is  the  certain  awakener  of  his 
musical  faculties  and  intelligence  with  which  at  the 
crucial  moment  his  face  will  not  fail  to  light  up.  Mel- 
ody, the  original  reporter  and  raison  d'etre  of  harmony, 
the  universal  voice  and  form  of  the  inner  music-con- 
sciousness, is  the  student's  natural  key  to  the  what, 
how  and  why  of  chords.  Melody  is  the  direct  re- 
porter of  fundamentals  and  chords.  Fundamentals 
and  chords  are  not  reporters  of  melody  though  they 
may  suggest  them.  The  common  practice  of  con- 
ceiving different  melodies  to  a  given  bass  belongs  to 
a  later  stage  in  study.  Thus  to  begin  the  study  of 
chords  is  to  reverse  the  natural  order. 

Below  are  examples  of  first  exercises  embodying  the 
primary  triads.  It  is  a  psychological  error  to  suppose 
that  any  beginner  however  gifted  possesses  the  con- 


280 


THE  NATURE  OF  MUSIC 


ceptive  power  to  grasp  the  four-voice  music-thought 
embodied  in  these  given  basses.  The  impossible  be- 
ing demanded,  the  student's  performance  is  neces- 
sarily mechanical  and  musically  dead  since  his  musical 
faculties  are  not  called  into  requisition.  How  many 
beginners  are  there  who  even  so  much  as  hear  the 
given  bass  itself!  Even  those  who  do,  what  musical 
sense  can  they  make  of  it,  what  harmonic  connection 
do  they  perceive  in  these  series  of  bass-tones  ?  None 
whatever.  Does  not  the  untrained  and  natural  bass- 
singer  feel  and  find  his  tones  in  relation  to  something 
else  which  he  grasps  and  remembers  as  a  whole, 
namely,  to  a  melody  ?  When  there  is  no  one  present 
to  sing  the  melody  what  does  this  natural  bass  do, 
does  he  sing  the  bass-part  ?  No,  he  sings  the  melody. 
Thus  cut  off  from  melody,  from  music-thought  by 
these  basses,  the  student's  only  intellectual  refuge 
lies  in  the  prescribed  rules  for  connecting  chords 
which  more  often  tell  him  what  not  to  do  rather  than 
what  to  do.  Even  though  he  performs  his  task  cor- 
rectly he  has  gained  nothing  musically,  and  the  edu- 
cational purpose  is  not  attained. 

1.  8  2.8 


-^:^ 


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75*- 


P=t 


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I      IV    I      VI       IVIIVVI 

The  same  material,  in  short,  the  same  exercises  are 
next  presented  in  the  form  of  melody,  of  music-thought 
itself. 


i 


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CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    281 

These  melodies  and  their  harmonic  index  plainly  set 
the  student's  task  before  him,  and  give  him  the  key  to 
the  whole  musical  rationale  of  the  situation.  Melody 
being  the  one  simple  and  real  fact  in  the  beginner's 
inner  consciousness  and  experience  of  music,  it  follows 
that  the  given  melody  is  the  one  thing  that  his  musical 
faculties  can  seize  upon  and  be  stirred  by,  the  one 
thing  that  lies  within  his  intellectual  grasp  and  appre- 
ciation, the  one  thing  he  appreciates  and  remembers 
as  a  whole  and  in  relation  to  which  it  is  easy  for  him 
to  add  something  else  since  it  explains  the  musical 
what,  how  and  why  of  the  addition.  The  beginner 
feels  and  can  follow  the  inherent  relations  connecting 
the  tones  of  the  given  melody,  he  readily  learns  to  hear 
the  concomitant  voices  reported  by  the  melody,  since 
those  voices  but  complete  the  sense  of  the  melody. 
Thus  as  he  adds  voice  upon  voice  the  student  duly 
learns  to  appreciate  the  concurrences  and  correla- 
tions of  all  the  four  voices,  in  fine,  he  knows  what 
he  is  about  and  attains  the  educational  purpose  of  the 
exercises.  Below  is  the  desired  result  of  his  perform- 
ance, valuable  if  worked  out  from  a  given  melody, 
valueless  if  worked  out  from  a  given  bass. 


2. 


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The  corresponding  material  in  minor  is  embodied 


282 


THE  NATURE  OF  MUSIC 


in  the  following  given  basses  at  a),  given  melodies  at 
6),  and  performances  at  c). 
1.  2. 

8  #  8  #  # 


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It  will  be  observed  that  the  above  exercises  are  the 
exact  counterparts  in  minor  of  those  just  presented 
in  major.  This  comparative  study  and  treatment  of 
corresponding  material  in  major  and  minor  by  means 
of  such  parallel  exercises  in  given  melodies  is  com- 
mended for  its  usefulness  to  students. 

Exercises  in  the  given  bass,  owing  to  their  arbitrary 
prescription  of  the  order  and  arrangement  of  material, 
completely  cut  off  the  student  from  that  independence 
of  thought  and  judgment  in  the  use  and  selection  of 
chord-material  which  is  so  essential  to  its  mastery. 
Not  so  with  exercises  in  given  melodies,  for  these  may 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    283 


be  presented  with  and  without  harmonic  prescriptions. 
For  illustration  we  will  take  the  first  of  the  above 
parallel  exercises  in  major  and  minor.  Present  these 
melodies  without  harmonic  numbers  and  ask  the 
student  for  their  harmonic  self-reports.  He  will 
respond  with  the  following:  — 

Major  Minor 

1113  1  X  X  X  3  X 


i 


I 


-<s- 


-^ 


Setting  out  with  a  distinct  perception  of  these  com- 
mon harmonic  reports  asserted  by  the  melody  itself 
the  student  has  a  great  advantage  for  he  is  thus 
enabled  to  distinguish  between  such  self-reports  of 
natural  harmony  and  the  personally  selected  reports 
of  selected  harmony.  In  short,  he  learns  what  is  the 
difference  between  self-reported  harmony  and  per- 
sonally selected  harmony,  between  reports  perceived 
and  reports  conceived,  all  of  which  he  cannot  learn 
from  a  given  bass.  Now  change  the  harmonic  num- 
bers of  these  parallel  exercises  as  follows  and  ask  the 
student  which  harmonies  are  self-reported  and  which 
are  selected. 


Major 


The  student  will  answer:  the  second  harmony  in 
both  exercises  is  selected,  all  the  others  are  self- 
reported.  Next  ask  the  student  to  conceive  other 
harmonizations  of  the  same  melodies  restricting  him- 
self of  course  to  the  ground  forms  of  the  primary 


1  5 

1  3 

1 

Minor 

1     5 

1  3 

1 

* 

•X- 

£84 


THE  NATURE  OF  MUSIC 


triads.     He  will  readily  think  out  the  following  con- 
nections of  harmonies :  — 


a)  Major: 

1  1 

5  3 

1 

Minor: 

1    1 

»  3 

' 

b)  Major: 

5  1 

5  3 

1 

Minor: 

5     1 

6   3 

1 

The  student  is  to  work  out  all  these  exercises  in  four 
voices  both  in  close  and  open  harmony.  Present  the 
chord-forms  6  and  % :  require  the  student  to  introduce 
them  in  these  same  exercises  placing  the  thorough- 
bass numbers  under  the  notes  of  the  melody.  He  will 
easily  produce  the  following  conceptions:  — 


a)  Major: 


1  1 

1  3 

1 

1    1 

1  3 

1 

c    c 

c     b 

c 

Minor: 

a    a 

a    g# 

a 

6 

I 

6 

I 

1  5 

1  3 

1 

1     6 

1  3 

1 

C     C 

c   b 
I 

c 

Minor: 

a    a 

a 

b)  Major: 


When  the  secondary  triads  are  introduced  the 
student  will  soon  find  the  right  place  for  the  subme- 
diant  in  the  same  melodies  as  follows :  See  asterisks. 


Major : 


These  illustrations  suffice  to  show  the  practical 
value  of  our  harmonic  numbers  as  here  applied  to 
melody,  the  natural  and  all-potential  harmonic  voice 
of  music.  Both  when  they  indicate  harmonic  self- 
reports  or  percepts  and  when  they  indicate  selective 
harmonic  reports  or  concepts,  they  directly  explain 
and  interpret  the  true  meaning  of  harmony  to  the 


1     3 

5  3 

1 

1  3 

5   3 

1 

c    c 

c     b 

c 

Minor : 

a    a 

a    g# 

a 

^ 

•Jf 

CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    285 

student's  musical  understanding.  In  fulfilment  of  an 
inherent  law,  melody  evolved  the  chord.  Nature  has 
bountifully  endowed  the  student  with  a  keen  sense  of 
that  inner  law  and  of  that  concomitant  harmony 
always  reported  by  and  inseparable  from  melody. 
The  genesis  and  development  of  harmony  being  due 
to  melody  it  lies  in  the  nature  of  things  that  the  study 
of  harmony  is  the  study  of  the  harmony  of  melody,  in 
a  word,  of  meloharmony. 

At  the  outset  the  student's  inner  consciousness  and 
experience  of  music  assumes  but  one  tangible  and 
graspable  form,  melody.  Nature's  gift  to  the  student 
is  an  inborn  appreciation  of  melody,  the  power  to 
follow  and  remember  a  melody  as  a  connected  whole 
and  therefore  the  power  to  turn  it  over  and  over  in  his 
mind  as  he  selects  this  or  that  series  of  chords  and 
musically  reflects  upon  this  or  that  way  of  leading  the 
voices.  Given  a  melody  to  harmonize,  the  student 
sets  out  with  the  one  thing  he  can  mentally  grasp;  he 
perfectly  comprehends  the  subject  of  his  work  and 
therefore  also  its  object.  Having  a  tangible  subject  he 
has  a  tangible  object ;  his  melody  is  his  preceptor  and 
guide  in  his  choice  of  harmonies,  explains  to  him  why 
now  a  root  or  fifth  or  third  is  doubled,  why  a  bond- 
tone  is  now  tied  and  now  not  tied,  why  an  upleader  is 
sometimes  not  resolved  but  led  downward  and  why 
the  downleader  is  often  treated  in  a  like  manner;  in 
short,  he  thinks  and  hears  everything  in  relation  to 
and  from  that  melody,  which  is  the  key  to  the  whole 
situation.  Harmonic  numbers  over  a  given  melody 
appeal  to  the  student's  musical  intelligence  and  rea- 
son.   Roman  numbers  under  a  given  bass  do  not.   The 


286  THE  NATURE  OF  MUSIC 

principles  of  music  are  inherent  in  and  assert  them- 
selves in  a  melody.  This  cannot  be  aflSrmed  of  a 
given  bass  except  when  the  melody  is  presented  in  the 
bass.  Thus  guided  through  melody  to  a  clear  per- 
ception of  the  operation  of  these  rhythmo-harmonic 
principles,  the  student  is  prepared  to  appreciate  that 
rules  apply  to  specific  cases  and  not  to  all  cases. 

Teachers  will  find  no  difficulty  in  preparing  work- 
ing-material for  students  in  the  form  of  given  melodies 
in  which  the  usual  chord-material  is  progressively 
introduced.  Besides  presenting  melodies  with  and 
without  harmonic  numbers  it  will  be  found  useful  to 
require  students  to  conceive  a  few  melodies  of  their 
own  which  shall  embody  the  material  of  each  lesson. 
It  is  also  suggested  that  the  work  should  introduce 
a  greater  variety  of  rhythmic  forms  than  is  usual. 
Exercises  in  the  earlier  stages  should  include  the  two 
forms  of  dual  subrhythm  or  measure,  light — heavy, 
heavy — light  and  the  three  forms  of  triple  subrhythm 
or  measure,  light — light — heavy,  light — heavy — light, 
heavy — light — light.  In  later  stages,  compound  and 
even  mixed  subrhythms  should  be  introduced.  In 
preceding  chapters  I  explained  the  original  and  in- 
separable correlations  of  rhythm  (form  and  relation 
in  time)  and  harmony  (form  and  relation  in  space)  of 
rhythmic  accents  and  harmonic  forms.  These  corre- 
lations obtain  in  selective  harmony  as  well  as  in  self- 
reported  harmony,  and  it  follows  that  the  study  of 
rhythm  is  as  essential  as  that  of  harmony.  A  series 
of  harmonies  occupies  a  series  of  rhythm-periods ;  the 
former  cannot  be  understood  apart  from  the  latter. 
Its  rhythm  is  the  foundation  of  a  music-concept  or 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN    287 

melody.  A  familiar  melody  is  recognized  when  its 
rhythm  is  tapped  by  the  fingers.  Melody  is  intoned 
rhythm.  Change  its  rhythm  and  you  produce  an- 
other, a  different  melody  out  of  the  same  series  of 
tones.  It  is  unscientific  and  untrue  to  speak  of  such 
a  changed  melody  as  the  same  melody  in  another 
rhythm.  In  forming  his  concept  of  a  melody  let  the 
student  begin  at  the  bottom  by  exaggerating  the  em- 
phasis of  its  rhythm.  Then  let  him  intone  the  rhythm. 
The  exaggerated  emphasis  will  then  plainly  report  the 
concomitant  harmonies  in  his  mind  and  guide  him  to 
a  satisfactory  result  in  his  selective  harmonization  of 
the  melody. 

There  are  other  advantages  of  exercises  in  given 
melody  which  do  not  exist  in  those  of  the  given  bass.  I 
will  stop  here  to  point  out  only  one.  It  is  this.  Given 
melodies  may  be  presented  in  every  voice,  not  only  in 
the  soprano,  but  in  the  bass,  tenor  and  alto  as  well. 
In  all  these  voices  the  student  will  comprehend  the 
melody  equally  well,  and  such  exercises  in  each  of  the 
four  voices  may  be  presented  from  the  start.  It  may 
be  objected  that  such  exercises  will  infringe  upon  the 
exclusive  and  erudite  domain  of  simple  counterpoint. 
Yes,  but  why  not.^  After  all,  is  that  domain  either 
so  exclusive  or  so  erudite  as  tradition  would  have  it 
appear  ?  In  all  forms  of  counterpoint  does  not  each 
tone  in  each  voice  report  a  root  or  third  or  fifth  or 
seventh  or  ninth,  a  consonance  or  a  dissonance  ?  After 
all  is  said  of  the  basic  importance  of  its  rhythm,  is  not 
all  counterpoint  a  question  of  harmony,  of  regnant 
harmony  and  byharmony,  of  regnant  tone  and  by- 
tone  ?     The  study  of  counterpoint  as  an  evolutionary 


288  THE  NATURE  OF  MUSIC 

chapter  in  history  is  one  thing;  the  study  of  counter- 
point as  an  art  to  be  mastered  or  a  necessary  part  of 
music  education  is  quite  another  thing.  This  art  of 
acquiring  independence  in  the  use  and  selection  of 
materia  musica  in  the  simpler  contrapuntal  forms 
should  not  be  put  off  until  the  student  has  worked  his 
way  through  an  entire  textbook  on  chords.  The  con- 
ventional cantus  firmus  is  but  a  melody,  and  every- 
thing that  is  to  be  added  to  the  melody  lies  in  it  and 
grows  out  of  it.  The  sooner  such  work  is  begun  the 
better.  Let  A,  B,  C  indicate  the  order  of  conceptive 
work  dealing  with  a  cantus.  A :  think  the  rhythm 
with  exaggerated  emphasis.  B:  intone  the  rhythm. 
C :  harmonize  the  intoned  rhythm.  Such  a  concept  is 
synthetic  and  complete  since  B  is  inseparably  asso- 
ciated with  A,  and  C  with  both  B  and  A.  Now  that 
we  have  discovered  in  one  voice  both  the  origin  of 
harmony  and  the  fundamental  principles  of  music, 
now  that  we  can  positively  affirm  that  melody  is  not 
an  element  but  an  indissoluble  composite  of  rhythm 
and  harmony  reporting  in  one  voice  now  a  consonance 
and  now  a  dissonance  and  that  music  had  its  genesis 
in  this  composite  voice  of  united  rhythm  and  harmony, 
now  that  we  are  able  to  view  and  study  the  material 
of  music  in  the  light  of  its  origin  and  can  trace  its 
development  since  we  can  learn  from  the  harmonic 
self-reports  of  homophonic  melodies  what  nature  has 
done  and  from  selective  harmony  what  art  has  done 
in  the  evolution  of  both  rhythmic  and  harmonic  mate- 
rial :  it  follows  by  implication  that  the  entire  rhy thmo- 
harmonic  materia  musica  both  as  applied  in  art  and 
in  textbooks  stands  forth  in  a  wholly  new  light.     A 


CHORDS  IN  THE  LIGHT  OF  THEIR  ORIGIN     289 

young  child  may  now  gain  as  perfect  an  intellectual 
grasp  of  the  rhythmo-harmonic  form  and  content  of 
a  melody  as  that  of  his  teacher.  Each  step  in  such 
analysis  renders  clearer  and  deeper  the  child's  musical 
appreciation,  since  it  directly  reports  and  causes  the 
child  to  realize  the  purely  miosical  content  of  a  melody. 
The  child  sets  out  with  a  purely  sensory  perception 
and  appreciation  of  melody:  through  rhythmo-har- 
monic analysis  this  perception  and  appreciation  are 
elevated  from  that  lowest  domain  of  mere  sensation 
to  the  higher  and  alone  dignified  domain  of  the 
intellect.  Thus  a  little  musical  savage  is  at  once 
metamorphosed  into  a  little  intelligent  musician. 
From  A  to  Z  the  study  of  music  is  the  study  of  the 
rhythm  and  harmony  of  melody.  Thus  from  the 
start  our  youngest  students  may  not  alone  really  study 
but  may  really  study  music  itself,  may  begin  and  con- 
tinue with  the  study  of  melody,  its  rhythm  and  its 
harmony.  Young  students  may  learn  to  appreciate 
and  perform  their  little  pieces  by  Bach,  Mozart  and 
Beethoven  with  the  same  adequate  intelligence  and 
consummate  art  with  which  mature  artists  produce 
the  more  complex  works  of  these  masters,  in  short,  so 
far  as  he  goes  the  student  may  be  an  intelligent  musi- 
cian and  a  true  artist.  Theory  and  practice  may  be 
united  from  the  start,  their  separation  is  a  thing  of  the 
past.  The  intellectual  appreciation  and  enjoyment 
of  music  may  in  consequence  spread  far  and  wide  and 
need  no  longer  be  regarded  as  an  exclusive  possession 
of  the  enlightened  few.  Than  music  no  art  is  more 
accessible  and  democratic,  therefore  less  esoteric. 


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68.     1  3     5      5    5 


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69.       5     3 


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|i      *     ^    \w 


I 


70.       1 


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3       5      5 


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2: 


71.     53       3       5       1      1 


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I 


2=i^ 


F=i«=«= 


f 


72. 


te 


73.      5  15  13     5     3 


BIRD  SONGS 


803 


74.       3   13  13     5 

m * 


i 


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m- 


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IV 


75.        1  1 


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76.      51        51        51        31 


^  n  -  n  -  n  ^s 


M 


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77.       1 


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78. 


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79.      1  5  5     1 


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80. 


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304 


THE  NATURE  OF  MUSIC 
81.  1  5      1 


M 


^^=w 


I 


I 


82. 


i 


I 


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83.     5  1 


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IV  VI 


86. 


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EXPLANATION  OF  SYMBOL  NUMBERS 

Roman  =  major  mode 
Italic    =  minor       " 

large  =  major  hartnony  or  chord 
small  =  minoT        "  "      ** 

large,  crossed  =  SLUgmented  chord 
^r(x5ic  =  harmonic  or  interval 

e,  g.  Y  =  major  dominant  harmony  or  chord  of  major  mode 
11  =  minor  supertonic  chord  of  major  mode 
V=  major  dominant  harmony  or  chord  of  minor  mode 
F=  minor         **  "         "       "      «      "  " 

TfZ=  augmented  mediant  chord  of  minor  mode 

^ .^^  5  =  fifth  of  major  harmony 

1^    «=    «     "  minor         « 


INDEX 


Accent,  31,  42-44,  99,  120;  efficient, 
24,  25,  27,  54,  55,  95,  102,  105, 108, 
109, 112, 113, 117, 125-127, 130-133, 
149,  176,  178,  188,  194,  206,  218, 
219;  measure,  149;  relative,  43,  44, 
99;  rhythmic,  12,  32,  46,  53, 107-109, 
286;  rhythmo-harmonic,  25,  105; 
syllabic,  149;  time-,  32. 

Acoustic  numbers,  227. 

Acoustic  series,  20,  227. 

Acoustic  theory,  230. 

Acoustics,  17,  227;  laws  of,  244;  physi- 
cal, 4,  19,20,  21,  70;  psychological, 
19. 

^Esthetics,10,  21,  22,  75. 

Alto,  278. 

Ambrosian  melodies,  147. 

Analysis,  acoustical,  9;  of  feeling,  9; 
harmonic,  58,  68,  83,  116,  137,  235, 
250,  259,  265,  272,  274,  275;  of  mu- 
sic, 28;  rhythmo-harmonic,  289. 

Aristides,  148. 

Aristotle,  148. 

Aristoxenus,  148. 

Arnold,  Matthew,  175. 

Bach,  5,  86,  98, 118, 146, 170, 174, 175, 

196-198,  289. 

Balance,  13,  31,  32,  42,  152,  162;  per- 
fect, 33,  41,  44;  relative,  44;  rhyth- 
mic, 31,  32. 

Balanced  motion,  10,  30,  33,  38,  162. 

Balanced  sound,  30,  33,  38. 

Balanced  time-periods,  32. 

Bass,  fundamental,  277-279;  given, 
279-285,  287;  thorough,  259,  267, 
269,  270,  274. 

Beat,  130,  163,  168. 

Beat-periods,  160,  162. 

Beethoven,  5,  132,  146,  150,  170,  174, 
175.  212,  213,  266,  276,  289. 


BerUoz,  49,  171. 

Biads,  245-247,  251-253;  compound, 

245-256;  in  minor,  248,  255,  256; 

parallel,  255. 
Bird -melodies,  116. 
Bird-songs,  56,  58,  59,  61,  171,  176. 
Bond-tone,  63,  76,  122,  123,  132,  136, 

190.  193,  235,  277;  original,  122. 
Brahms.  49,  171. 

Bychord,  141. 

Byharmony,  106, 109-113,116,117,126, 
127, 141, 187,  205,  287;  relative.  111. 

Bytone,  106,  107,  109-113,  116-123, 
126,  127,  132,  194.  198,  199,  201, 
203,  204,  206-210,  255,  256,  261; 
diatonic,  118-120;  report  (harmonic, 
self-)  of,  118,  119,  219;=  (tone-ca- 
dence), 121. 

Cadence,  29,  54,  56,  69,  103,  122,  129, 
142,  177,  180,  206,  208,  211,  214, 
216,  223;  closing,  123;  double,  136, 
192;  faUing,  92,  97,  136,  187,  190; 
five  original  cadences,  91-96;  harmo- 
nic, 130, 131, 133;  original,  of  Minor 
Mode,  185-198;  prototype,  185, 192; 
rhythm-,  42-45,  50,  53,  67,  111,  120, 
121;  rising,  92,  97,  136,  275;  single, 
136;  thread  of  harmony,  54;  tone-, 
45-48,  55,  86,  91,  121. 

Cadence-chord,  99. 

Cadence-harmony,  45-48,  58,  62,  111; 
original,  45-47;  genesis  of,  61-67. 

Cadence-moment,  42,  44. 

Cadence-relation,  113. 

Cadence-repose,  43,  53. 

Cadence-tone,  46,  47,  57-59,  61-66, 
92,  96-100,  106,  107,  113,  135,  136, 

191,  192,  235,  257;  (prototype),  191, 
194,  208;  (original),  46,  92,  98, 106, 
135,  136. 


308 


INDEX 


Calls  and  cries,  56. 

Canon,  181. 

Cantata,  157. 

Canticle,  157. 

Cantus-firmus,  288. 

Cardinal  principle,  15,  21,  24,  28, 162. 

Carlyle,  159. 

Chant,  antiphonal,  181 ;  primitive,  165. 

China,  16,  17,  212. 

Chopin,  169,  171,  212. 

Chord,  3, 4, 11, 20, 37, 49-51,  61,  62, 71, 
73, 84,  90, 92, 102, 104, 134, 135, 137, 
143, 149, 191,  209,  231,  233,  234,  236, 
266,  278-280,  284,  285,  288;  aug- 
mented, 249,  262;  cadence-,  99;  com- 
ponents of,  89,  91,  242,  245,  259; 
compound,  90,  141,  237,  240,  243- 
245, 248, 255-257,  259-263,  272,  274; 
consonant  or  dissonant,  232,  245; 
derived  from  the  original  consonance 
and  dissonance  in  one  voice,  133-141 ; 
from  the  minor  forms  of  consonance 
and  dissonance  in  one  voice,  231-236 ; 
diatonic,  202;  diminished  seventh-, 
234,  239,  240,  260;  diminished-di- 
minished seventh-,  240 ;  diminished-, 
small  seventh-,  240;  dissonant,  144, 
232,  245 ;  dominant-seventh-,  84, 239; 
double,  211,  212;  fourth-sixth-,  238; 
ground-seventh-,  240;  harmonic  re- 
port of,  138,  139,  141,  234,  245,  259, 
266;  large  ninth-,  240-242;  large 
third-,  249;  major,  227;  major-small 
seventh-,  239;  major  subtonic-sev- 
enth-,  239 ;  major  tonic-seventh-,  255 ; 
minor,  177,227;  minor  ninth-,  139, 
140,  141,  234,  240-244,  247,  275; 
minor  subtonic-,  seventh-,  239 ;  minor 
tonic-seventh-,  255 ;  ninth-,  240-244 ; 
passing,  275;  primary,  133,  248;  re- 
pose-, 99;  secondary,  248;  secondary 
ninth-,  256;  secondary  seventh-,  253, 
255,  268;  self-reports  of  a,  233,  234, 
847,  255;  seventh-,  84, 139,  140,  234, 
238-242  244, 247,  253,  255,  256,  260, 
268-270;  simple,  90,  141,  144,  243- 
245,  248,  249,  251-253,  256;  simple 


and    compound,  defined,    243-276; 

sixth-,  238;   small  ninth-,  240-242; 

subdominant-seventh-,  254 ;  submedi- 

ant-seventh-,  254,  256;  subsecond-, 

261,   262,    265,   267-270;   subtonic- 

seventh-,  235,  254 ;  supersixth-,  261- 

264,    267-271 ;    supertonic-seventh-, 

254;  tone-,  86;  tonic-,  66. 
Chord-analysis,  68,  135. 
Chord-basis  of  harmony,  69. 
Chord-building,  140,  244. 
Chord-cadence,  99,  136. 
Chord -conception  of  harmony,  86. 
Chord-concepts,  91. 
Chord-fifth,    234,  238,  240,   241,  248, 

275. 
Chord  of  the  fifth-sixth,  240. 
Chord-forms,  71,  72, 135,  139. 
Chord-harmony,  68-74,  147. 
Chord-intervals,  89-91,  136,  137,  232, 

237,  249. 
Chord  of  the  major  ninth,  84. 
Chord-material,   233,   277,   278,  282, 

286. 
Chord-ninth,  275. 
Chord-position,  240-243,  266. 
Chord  prototype,  140. 
Chord-root,  135,  136,  140,  232,  234, 

237-243,  245,  248, 249,  258-261,  268, 

274,  275,  278. 
Chord  of  the  second,  240. 
Chord-seventh,  268,  275. 
Chord-sixth,  248. 
Chord-structure,  242,    257,   261,  263, 

264,  265,  268,  271,  272. 
Chord-theories,  89,  230. 
Chord-third,  234,  238,  240,  241,  248, 

274. 
Chord  of  the  third-fourth,  240. 
Chord  type,  239. 
Chromatic,  39,  59,  93,  124,  132,  187, 

190,   193,  201-204,   215,  219,  220, 

221. 
Chromatic  scale-system,  95. 
Classics,  49. 
Composer,  75, 104,  150. 157,  159,  171, 

172,  175,  217,  261. 


INDEX 


309 


Concept,  26,  44.  62,  78,  79,  139,  179, 
181,  284,  287,  288;  harmonic,  76,  91 ; 
music,  286. 

Concerto,  146;  piano-,  276. 

Concomitants,  34,  37,  40,  45,  59,  62,  75, 
79,  113-115,  117,  124,  131,  140,  148, 
149,  193,  194,  202,  206. 

Confucius,  16. 

Consonance,  4,  7-9,  18-21,  26,  27,  45, 
50,  53-56,  61-64,  66-69,  75,  77,  85, 
86,  102,  112,  113,  115,  117,  120,  124, 
125, 127, 133, 141, 148, 165, 178, 189, 
192,  205,  214,  222,  223,  287,  288; 
major,  7,  33-36,  40,  41,  45,  46,  55, 
91,  95,  111,  124,  176,  177,  179,  180, 
190,  204,  217,  219,  221-223;  minor, 
59,  91,  177-180,  183-185,  190,  201, 
203,  214-218,  221-223,  231 ;  origin  of 
minor,  176-184;  prototype,  95,  124, 
133,  184,  185,  221,  231. 

Consonance  thread,  37, 143. 

Cotta  edition,  276. 

Counterpoint,  287. 

Dance,  4,  43,  116,  172. 

Diatonic,  192,  220,  221;  seven,  46,  75, 
85,  94,  117,  122,  141,  142,  144. 

Diatonic  bytone,  118-120,  208,  210, 
218. 

Diatonic  cadence,  98,  99. 

Diatonic  chord,  202. 

Diatonic  division  of  octave,  95. 

Diatonic  harmony,  124,  125,  201,  203, 
205,  216-218. 

Diatonic  major  relation,  123,  134. 

Diatonic  major  triad,  133. 

Diatonic  melody,  99. 

Diatonic  minor,  201-203,  235. 

Diatonic  minor  melody,  202,  216. 

Diatonic  scale,  144. 

Diatonic  scale-system,  95. 

Diatonic  stage  of  tonality,  95. 

Dissonance,  4,  7,  8,  18-21,  26,  27,  45, 
50,  53,  69,  75,  86,  112,  113,  115,  116, 
123-125, 133, 141, 148, 149, 180, 189, 
205,  287,  288;  acoustical,  9;  five- 
tone,    95,  221;    four-tone,  95,  117, 


221 ;  genesis  of,  103,  120;  genesis  of 
original,  in  one  voice,  61-67;  latent 
feeUng  of,  46, 54, 55 ;  major,  124, 180, 
190,  209,  214,  222,  223,  231 ;  minor, 
185, 188, 190, 198,  214,  222,  223,  231 ; 
one  voice,  7,  62,  68,  91, 102;  origin  in 
one  voice  of  the  minor  form  of,  185- 
198;  original,  9,  35,  55,  77,  85,  91, 
103,  111;  prototype,  95,  124,  134, 
185, 188,  221,  231 ;  regnant,  127, 128. 

Dominant,  major,  47,  63,  67,  77,  188, 
189,  206,  207,  239,  249,  262;  major 
ninth  of,  76,  82;  major  third  of,  76,. 
82;  minor,  201,  216-218,  262;  minor 
seventh  of,  76 ;  prototype,  206 ;  pure 
fifth  of,  76,  82;  regnant,  188,  207, 
210;  regnant  minor,  188,  206-218; 
rhythmic,  120;  small  ninth-chord  of, 
275. 

Dominant-fifth,  76. 

Dominant-harmony,  58,  60,  61,  65,  75, 
77,  83,  &4,  90,  93,  108,  183,  187-189, 
198,  249. 

Dominant-ninth,  76. 

Dominant-root,  76,  81,  88,  89. 

Dominant-seventh,  76. 

Dominant-seventh-chord,  84,  239. 

Dominant- third,  76. 

Dominant-thread,  47,  82,  84. 

Dominant-triad,  84,  235,  249. 

Dorian  scale,  229. 

Downleader,  62,  64,  92,  95,  183,  285; 
chromatic,  275;  prototype,  95,  192. 

Drama,  156,  157. 

Dreiklang,  269. 

Drum,  165,  166. 

Duplicates,  27,  71,  184,  185;  221.  231. 

Dynamics,  125. 

Ear,  20,  73,  44,  77,  78,  86,  260,  268. 

Ecclesiastical  melodies,  116. 

Ecclesiastical  music,  148. 

Elements,  2,  6,  41,  44,  50,  67,  74,  79, 
130,  150,  176,  180;  concurrence  of, 
129;  succession  of,  129;  union  of,  6, 
8. 

Elements  of  music,  3,  7,  23,  48,  56. 


310 


INDEX 


Elevenths,  89,  93. 
Enharmonic  harmonies,  271,  274. 
Enharmonic  scale-system,  95. 
Enharmonic  stage  of  tonality,  95. 
Equilibrium,  10-14,  21,  24,  28,  30,  31, 

33,  41-43,  48,  51,  112,  113,  151,  153, 
164;  cardinal  principle,  36,  162;  = 
(harmony),  10-15, 30 ;  harmonic,  125 ; 
relative,  133;  rhythmic,  125;  rhyth- 
mo-harmonic,  125;=  shaping  princi- 
ple, 10,  11,  24,  41,  51,  120,  130,  195; 
stable,  43,  54,  67,  116,  127,  178;  un- 
stable, 43,  54,  67,  116. 

Evolution,  1,  4,  5, 13, 15, 16,  39,  56,  70, 
94,  96,  103,  104,  110,  130,  176,  177, 
193,  215,  223-225,  233;  harmonic, 
40-42,  104,  225. 

Evolution  of  perception,  52,  165. 

Expansion  of  subrhythm  and  rhythm, 
160-175. 

Eye,  73,  74,  260,  268. 

Feeling,  26,  34,  36,  40,  41,  44,  60,  68, 

72,  79,  80,  178,  184;  (common,  com- 
mon music-,  music-),  2,  5,  6,  8-10, 
13,  15,  16,  18-21,  24,  28,  29,  32,  33, 
35,  37,  43,  45,  51-53,  62,  66,  69,  76, 
78,  86,  88,  91, 104, 108,  139,140, 147, 
153, 161, 176, 179, 181, 197,  226,  228; 
common  report  of  common,  17-22, 
108,  147;  rhythm-harmonic,  278; 
tone-rhythmic,  10,  11,  12. 

Feeling  of  cadence,  62. 

Feeling  of  dissonance,  46,  54,  55. 

Feeling  of  music  per  se,  7,  9,  22. 

Feeling  of  rhythm,  33. 

Feeling  of  repose,  62. 

Fifth,  25-27,  29,  30,  35,  37,  40,  41,  47, 
59,  60,  63,  67,  84,  85,  89,  108,  123, 
138,  140,  179,  187,  200,  206,  217, 
285,  287;  chord-,  234,  238,  240,  241, 
248,  275;  consecutive,  277;  dimin- 
ished, 137,  234;  harmonic,  135,  234; 
large,  223,  224;  parallel,  131;  pure, 

34,  36,  61,  76-78,  81,82,  120,  137; 
small,  223. 

Folk-melody,  172,  174. 


Folk-song,  4,  15,  16,  77,  79,  81,  84, 
116,  172. 

Form,  5,  7-15,  17,  21,  24,  28,  49,  51, 
66,  68,  70,  75,  79,  83,  85,  89,  90,  99, 
103,  104,  133, 134, 145,  155, 160-162, 
165,  167,  170,  171,  173,  178-180, 
206,  216,  217,  219,  220,  221,  224, 
232,  234;  chord,  71,  72;  classic,  160- 
175;elemental,  20,  22,  30;  harmonic, 
4, 8,  9, 10, 23, 25,  30, 33-35, 41, 42, 45, 
48,  50,  62,  67,  73,  83,  93,  111,  112, 
122,  124,  129,  139,  182,  214,  233, 
286 ;  prototype  of  harmonic,  95 ;  orig- 
inal harmonic,  26,  95;  rhythmic,  23, 
32,  44,  50,  111,  129,  130,  164,  168, 
286;  rhythmo-harmonic,  24,  279, 288; 
space-,  14;  time-,  14;  tone-rhythmic, 
8;  universal,  7,  12,  43. 

Form  of  consonance,  7,  8,  53,  116,  125, 
184,  185,  204,  205,  214,  222,  223, 231. 

Form  of  dissonance,  7,8,53,116,125, 
214,  222,  223,  227,  231. 

Form  of  regnant  minor  dominant,  216- 
218. 

Form  in  space,  13,  104. 

Form  in  time,  13, 104. 

Fourth,  36,  59;  augmented,  138;  pure, 
137,  138. 

Fugue,  181. 

Fugue-subject,  118. 

Fugue-theme,  198. 

Fundamental  bass,  277-279. 

Fundamental  forms  of  harmony,   85. 

Fundamental  forms  of  tone,  53. 

Fundamental  principles,  8,  175,  288. 

Gevaert,  146. 
Given  bass,  285-287. 
Goethe,  11,  14. 
Greece,  16,  17. 
Greek  melodies,  146-149. 
Greek  modes,  145,  146. 
Gregorian  chants,  148,  149. 
Gregorian  melodies,  147. 

Harmonic,  34-36,  41,  45;  compound, 
90,  263;  concomitant.  59,  62;  double. 


INDEX 


811 


211,  248;  elementary,  35,  37,  40,  41, 
193;  simple,  90,  263. 

Harmonization,  74,  149,  156,  287. 

Harmony,  1-7, 9, 13, 19,  20,  21,  24,  33- 
35,  49,  51,  52,  63,  75,  76,  79,  86,  90, 
93,  99,  103,  120,  122,  129,  135,  136, 
138,  142,  144,  150,  154,  156,  158, 
159,  171-173,  177,  178,  185,  189, 
190,  197,  199,  206,  210,  213,  215, 
217,  218,  221,  226,  242,  243,  248, 
256,  269,  279,  283-289;  acoustic 
theory  of,  230;  basis  of,  33,  68,  69, 
102;  cadence-,  45-48,  58,62,  111; 
chord-,  68-74,  147;  chromatic,  201, 
202,  205,  219,  220.  271;  compound 
of,  263,  265,  266,  270;  concomitants 
of,  131,  140,  148,  149,  202,  211,  224, 
284,  285,  287;  =  (consonance),  91; 
contrapuntal,  70;  diatonic-,  118, 124, 
140,  201-203,  205,  216,  218;  =  (dis- 
sonance), 91;  dominant-.  58,  60,  61, 
65, 75, 77, 83, 84, 90, 93, 108, 183, 187- 
189,  198,  249;  double,  211,  212;  du- 
plicate forms  of,  184,  185;  =  equilib- 
rium, 10-15,  30,  150,  151;  enhar- 
monic, 271,  274;  expansion  of,  77, 
110;  evolution  of,  103,  176,  224,  233; 
five  components  of,  89-91;  genesis 
of,  54, 102, 109;  homophonic,  70, 102, 

105,  205,  229, 230;  major,  185;  major 
tonic-,  54-57-61,  64,  65,  91,  98,  105, 

106,  183,  184,  193,  229;  minor,  124, 
139, 185 ;  minor  tonic-,  178-180, 184- 
187,  198,  214,  221,  230;  multi-voice, 
75,  147;  original  (in  one  voice),  4, 
24,  25,  28,  36-40,  47,  49,  50,  61,  64, 
66-71,  73-75,  85,  87,  88,  102,  104, 
124, 133, 139-141, 147-149, 182, 184, 
211,  244;  original  cadence-,  45-47; 
original  forms  of,  184-185;  personal, 
71, 283 ;  polyphonic,  70 ;  potential,  26- 
27,  74,  77,  110, 181 ;  regnant,  24,  25, 
53-55,  58,  60,  65,  67,  83-85,  88,  98, 
104-113,  115-118, 125-127, 129-133, 
141, 149, 183, 186, 188, 193,  194, 198, 
201,  208,  209,  214,  220,  221,  223,  224, 
255, 261-264,  267,  268,  272-276,  287; 


relative,  54,  55,  111 ;  repose-,  45-48, 
62,  111 ;  selective,  286;  subdominant, 
58,  60,  61,  108,  198,  248;  tiieory  of, 
51 ;  thread  of,  35, 37, 38, 41, 54,  63, 79, 
80,  81,  84,  96, 107, 109, 124, 133, 134, 
137, 139-141, 143, 178, 183, 188, 193, 
224;  =  tone,  23,  28;  tone-rhythmic, 
10;  tonic-,  33,  45,  54,  56-58,  60,  61, 
64,  65,  83,  84,  93, 106, 179,  183,  186, 
187,  193,  214,  229,  230,  249,  260; 
treatise  on,  19,  68,  244. 

Harmony  of  sound,  23,  75,  147. 

Hauptmann,  M.  19,  244. 

Haydn,  174. 

History,  4,  40,  65,  66,  68,  111,  165. 

Homer,  16. 

Homophony,  4-6,  7,  68,  102-105, 
194,  195,  202,  223,  226,  232-234, 
249. 

Instrument,  165,  166. 

Interval,  36,  59,  76,  88,  89,  93,  96, 113- 
115,  138,  187,  189;  chord-,  91,  137; 
diminished,  93;  evolutionary  se- 
quence of,  60;  harmonic,  91, 136, 137, 
232;  major,  75,  139;  minor,  75, 
139. 

Interval  of  concurrence,  137. 

Interval-number,  93,  139. 

Interval-relation,  80. 

Interval  of  succession,  137. 

Key,  48,  61,  87,  96,  239,  262;  fifth  re- 
lated, 123;  interharmonic  relations  of 
one,  94. 

Key-centre,  220. 

Keynote,  27,  60. 

Key-relation,  60,  88. 

Leading  tone,  61. 
Liszt,  49,  203. 

MacDowell,  49. 

Major,   cadence -seventh -chord,    1S5; 

pure  diatonic,  203. 
Major  chord,  227,  232. 
Major  consonance,  7, 33-36, 40, 41, 45, 


sn 


INDEX 


46, 55,  91,  95,  111,  124, 176,  177, 179, 
180,  190,  204,  219,  221,  223  (origi- 
nal), 35,  55. 

Major  dissonance,  124,  180,  190,  209, 
214,  222,  223,  231. 

Major  dominant,  47,  63,  67,  77,  188, 
189,  206,  207,  239,  249,  262. 

Major  dominant-harmony,  183,  187, 
189. 

Major  dominant-thread,  235. 

Major  downleader,  192. 

Major  harmony,  185. 

Major  mode,  33,  41,  46,  56,  75,  85,  88, 

91,  95,  124,  139-141,  176,  178,  181, 
182,  186,  187,  191,  210,  214,  215, 
236;  (prototype),  95,  180,  181,  185, 
191,  200,  214. 

Major  ninth,  76,  77,  82,  137. 

Major  second,  255. 

Major  sixth.  36,  138. 

Major  subdominant,  188. 

Major  subdominant  harmony,  187. 

Major     subdominant  -  seventh  -  chord, 

254. 
Major  subdominant  triad,  235. 
Major  submediant-seventh-chord,  254. 
Major  subtonic,  253,  256. 
Major  supertonic  triad,  251. 
Major  tenth,  36. 
Major  tetrachord,  214. 
Major  third,  34,  36,  61,  76-78,  81,  82, 

120,  137,  138. 
Major  tonality,  67. 
Major  tonic,  41,  47,  60,  63,  65,  67,  77, 

92,  98,  103,  105-108,  111,  180,  181, 
185. 

Major  tonic-harmony,  54,  57-61,   64, 

65,  91,  98,  105,  106,  183,  184,  193, 

229. 
Major  triad,  90,  133,    237,  251,  262, 

268. 
Major  upleader,  187,  192. 
Measure,  168,  286;   dual,   161,   168; 

triple,  161. 
Measure-period,  162,  260,  261. 
Medicant,  144. 
Medicant  scale,  146. 


Medicant-triad,  248-250. 

Meistersinger,  146. 

Melody,  1-6,  9,  14,  15,  24,  25,  28,  37, 
39,  40,  41,  47-52,  54,  56,  60,  64,  67, 
71,  72,  74,  78,  79,  85,  91,  93,  98-100, 
121,  124,  130,  132,  140,  147,  148, 
154,  155,  172,  177,  178,  180,  186, 
187, 192,  193, 197, 198,  200,  202,  203, 
205,  206,  208,  209,  211,  214-217, 
220-224,  276,  280,  281,  284-289; 
analysis  of,  65;  ancient,  149;  a  com- 
posite, not  an  element,  23,  24 ;  bird-, 
116,  183;  ecclesiastical,  116;  embry- 
onic, 106;  folk-,  184;  Greek-,  116, 
149;  homophonic,  6,  24,  215,  223, 
227,  230,  233,  288;  mediaeval,  4; 
minor,  221;  modern,  182;  penta- 
tonic  stage  of,  113;  primitive,  64, 
104,  109,  176,  182-184,  225;  pure 
diatonic  minor,  216;  regnant  har- 
mony of,  102-175. 

Meloharmonic  phrase,  187. 

Meloharmonic  point,  120,  142. 

Meloharmonic  resolution,  142. 

Meloharmony,  24,  104,  120,  142,  197, 
285. 

Mese,  148. 

Metre,  33,  168. 

Minor,  123, 139, 195,  209;  imitation  of 
major,  180,  181, 185-187,  200,  205, 
214;  inverted  major,  227;  origin  and 
nature  of,  176-184;  pendant,  181, 
226,  228,  230;  pure  diatonic,  202, 
203,  216;  relative,  181. 

Minor  cadence,  180,  192. 

Minor  cadence-tone,  186-188. 

Minor  consonance,  59,  91,  177-180, 
183-185,  190.  201,  203,  214-218, 
221-223,  231;  (origin  of),  176-184. 

Minor  dissonance,  185,  188,  190,  198, 
214,  222,  223,  231. 

Minor  dominant,  187-189,  198,  200, 
201-203,  204,  206-218,  220. 

Minor  dominant-triad,  235. 

Minor  downleader,  192. 

Minor  forms  of  consonance  and  disso- 
nance, 185,  214,  222,  223,  231. 


INDEX 


313 


Minor  harmony,  124, 139, 185. 

Minor  harmonic  percept,  214,  236. 

Minor  melodic  scale,  201,  203. 

Minor  mode,  56,  59,  91,  124,  135,  141, 
177-179, 181, 182, 186, 187, 191, 196, 
205,  210,  214,  217,  236. 

Minor  root,  180. 

Minor  seventh,  38,  76-78,  137. 

Minor  sixth,  138. 

Minor  small  third,  180,  184,  200. 

Minor  subdominant,  187, 188, 204,  218, 
222. 

Minor  subdominant  harmony,  187, 188, 
198,  204,  218,  219,  222. 

Minor  subdominant  triad,  235. 

Minor  subtonic,  253,  256. 

Minor  subtonic-seventh-chord,  235. 

Minor  tenth,  36. 

Minor  tetrachord,  214. 

Minor  third,  36,  137,  138. 

Minor  tonic,  180,  181,  185,  198,  200, 
216,  220. 

Minor  tonic-harmony,  178-180,  184- 
187,  198,  214. 

Minor  triad,  228,  231,  236,  237,  268. 

Minor  upleader,  187,  192, 

Mode,  defined,  91-98;  major,  33,  41, 
46,  56,  75,  85,  88,  91,  95,  124,  139- 
141,  176,  178,  181,  182,  186,  187, 
191,  210,  214,  215,  236;  minor,  5Q, 
59,  91,  124,  135,  141,  177-179,  181, 
182,  186,  187,  191,  196,  205,  210, 
214,  217,  236;  prototype  major,  95, 
180,  181,  185,  191,  200,  214. 

Mode-idea,  85,  92,  94. 

Mode-relation,  88,  91,  94,  108,  180. 

Mode-tones,  87,  93,  94. 

Modes,  48;  ancient,  147;  Greek-,  145, 
146. 

Modulation,  183,  220. 

Moment,  musical,  149-160;  rhythmic, 
32,  38,  44,  51,  151;  rhythmo-har- 
monic,  23. 

Motion,  balanced,  10,  30,  33,  38,  162. 

Motive,  23,  44,  152,  153,  214. 

Mozart,  25,  170,  174,  289. 

Music,  absolute,  157;  analysis  of,  28, 


66;  art-,  15;  basis  of,  19,  20,  28, 
56,  58,  85,  102,  223;  books  on. 
181;  chorded,  4,  141,  215,  223,  224, 
235;  classic  form,  173-175;  concrete, 
233;  development  of,  9,  66,  105,  111, 
166,  171,  175;  elemental  form  of, 
22;  essence  of,  2,  3,  9,  14,  49, 
104;  evolution  of,  1,  15,  49,  107, 
220;  first  regnant  harmony  of,  55, 
61,  83;  five  original  cadences  of, 
92;  form  of,  5,  7,  9,  15,  21;  genesis 
of,  1,  4,  6-8, 10, 14, 15 ;  instrumental, 
166,  243;  message  of,  10,  14,  22, 
158;  messenger  of,  10,  14,  22,  149; 
modem,  4,  16,  70, 104, 116, 172-174, 
203,  212,  215;  multi-voice,  25,  85, 
116, 161,  223,  224,  226,  233;  nature-, 
15,  16,  17;  one,  15,  16,  17,  28;  one- 
voice,  4,  24,  25,  39,  45,  70,  85, 
102,  116,  147,  148,  194,  223;  origin 
of,  6-8,  9,  33;  pleasure  in,  28,  78, 
165;  polyphonic,  1,  97,  223,  224; 
primitive,  56,  66,  86,  104,  110,  116, 
165;  principle  of,  3,  7,  8,  15,  21,  22, 
24,  50,  149;  rationale  of,  17;  seven 
octaves  of,  141;  stages  of,  1,  6,  70, 
103;  study  of,  1,  6,  21,  28,  289; 
voice  of,  8,  23,  28,  33,  152,  153,  205, 
284. 

Music  of  antiquity,  147. 

Music-archgeologist,  202. 

Music  art,  15,  16,  49,  100,  110,  154. 
155,  158,  166,  171,  175,  289. 

Music-concept,  286. 

Music-consciousness,  6,  278,  285. 

Music-culture,  175. 

Music-drama,  156,  157. 

Music-education,  40,  234. 

Music-feeling,  2,  5,  6,  8-10,  13,  15,  16, 
18,  20,  21,  28,  32,  52,  53,  66,  69,  78, 
147,  153,  161,  181,  197,  226. 

Music-history,  3,  40   65,  66,  68,  165. 

Music-lesson,  98-100,  277;  work  for 
students,  101,  164,  282-288. 

Music  perse,  7,  9,  21,  22,  67,  110. 

Music-score,  268. 

Music-sense,  165. 


314 


INDEX 


Music-structure,  15, 173, 181,  270. 
Music-theory,  3, 16,  20,  51,  69,  70,  230, 

234. 
Music-thought,  23,  24,  161,  171,  280. 
Music-works,  13,  159,  170. 
Musician,  2,  39,  51,  57,  66,  100,  159, 

234,  289. 

Ninth,  25-27,  29,  38,  41,  47,  63,  67,  76, 
77,  81,  82,  85,  89, 118,  137,  180,  189, 
202-210,  223,  287;  harmonic,  234; 
large,  223;  original,  253;  prototype, 
208;small,  223,  260. 

Notation,  60, 65, 229, 275,  276 ;  staff,  88. 

Nucleus,  141 ;  septonal,  142. 

Nucleus-triad,  261-264,  268,  269. 

Numbers,  89,  90;  acoustic,  227;  ele- 
mentary group-,  167;  harmonic,  37, 
47,  58,  61,  63,  64,  71,  74,  75,  78,  80, 
86-88,  93,  99,  100,  137,  139,  179, 
185,  186,  189,  214,  222,  232,  283- 
286;  interval,  93,  139;  percept,  246; 
rhythm,  161;  scale,  86-88,  94;  tho- 
rough-bass, 238,  284. 

Octave,  34,  35,  59, 81,  95, 118, 131, 141, 

143,  200;  consecutive,  277;  parallel, 

231 ;  pure,  36. 
Octonal  scale,  144,  146. 
Octonal  terminal,  144. 
Opera,  157. 
Orchestra,  166. 
Organ,  166. 
Original  harmony  in  one  voice,  28,  39, 

40,  47,  50,  64,  66-69,  73,  75,  85,  88, 

104,  124,  133,  140,  148. 
Overtones,  20,  227. 

Pedagogy,  277,  278. 

Pentatonic  melody,  109,  186. 

Pentatonic  period,  183. 

Pentatonic  scale,  64,  65, 109. 

Pentatonic  stage  of  melody,  108-110, 
113,  114. 

Percept,  26,  41,  44,  82,  284;  five  origi- 
nal harmonic,  77,  84,  85,  95,  122, 
224,  227,  235,  249;  prototype,  95; 


harmonic,  26,  27,  36,  38,  61,  76,  77, 

85,  87,  89,  95,  103,  122,  179,  182, 
187,  200,  222-225,  234,  235,  275; 
harmonic,  of  minor  origin,  222-224; 
major  harmonic,  179, 222,  229;  minor 
harmonic,  179,  200,  214,  216,  222, 
229,  230. 

Percept-numbers,  246. 

Perception,  21,  28,  41,  53,  68,  73,  79, 
93, 165, 166, 178, 197,  228;  common, 
19,  20,  22,  29,  37,  43,  45,  64,  66,  69, 

86,  89,  91,  108,  179,  181 ;  evolution 
of,  52,  110;  harmonic,  78,  106,  110, 
111,  230. 

Perception  of  harmony,  24,  110,  111, 
182. 

Perception  of  relation,  76,  139. 

Perception  of  rhythm,  33,  44. 

Period,  42,  125,  152,  160,  161,  162, 
165,  173,  182;  beat-,  160-163;  ca- 
dence-, 121;  dual,  29,  162;  elemen- 
tary, 170,  measure-,  162,  260,  261 
repose-,  121;  rhythmic,  12,  42,  88 
120,  121,  127-130,  217;  rhythm-,  12 
32,  33,  125,  127,  129,  153,' 193,  250 
286;  subbeat-,  160,  subrhythmic,  163 
168;  time-,  32,  33,  38;  triple-,  29. 

Personal  election,  25. 

Personal  element  of  choice,  5. 

Personal  equation,  5,  40,  70,  71,  205, 
215,  230. 

Personal  prejudice,  5. 

Personal  selection,  71,  72,  75,  85,  177, 
230. 

Peters'  edition,  276. 

Phrase,  16,  80,  122, 130,  152, 161,  162, 
171-173,  187,  278. 

Physical  acoustics,  20,  21,  70. 

Physical  tone,  20. 

Piano-concerto,  276. 

Pianoforte,  95,  96,  166. 

Pitch,  20,  30,  33,  34,  36,  53-55,  60,  61, 

87,  88,  94,  143,  148,  186;  fixed,  60. 
Pitch  relation,  60,  88,  99,  141,  233. 
Plagal  ending,  136,  235. 
Polyphony,  4,  103,  140,  215,  223,  224, 

235. 


INDEX 


315 


Potential  harmony,  26,  27,  74,  77, 110, 
181;  principle  of,  26,  27. 

Primes,  93. 

Principle,  3,  7,  12-14,  16,  17,  19,  21, 
22,  40,  47,  65,  66,  140,  151, 166, 182, 
197,  198,  200;  cardinal-,  15,  21,  28; 
fundamental,  8,  175;  rhythmo-har- 
monic,  286;  shaping,  10,  11,  24,  28, 
31-33,  36,  41,  48,  50,  51,  120,  130, 
149, 161, 162, 171-173, 195;  miiversal, 
of  form  and  relation,  12-14. 

Principle  of  harmonic  genesis,  27,  38, 
65, 105, 125, 181. 

Principle  of  music,  3,  7,  8,  15,  21,  22, 
24,  50,  149. 

Principle  of  potential  harmony,  26,  27. 

Principle  of  tone  genesis,  95. 

Progression,  13,  48,  96-98,  112,  113, 
115,119,142,  152,  187,192,220,275. 

Prototype,  95,  124. 

Prototype  cadence,  185,  192. 

Prototype  cadence-tone,  191,  194,  208. 

Prototype  chord,  140. 

Prototype   consonance,    95,    124,   133, 

184,  185,  221,  231. 

Prototype  dissonance,  95, 124, 134,  185, 
188,  221,  231. 

Prototype  dominant,  206. 

Prototype  downleader,  95, 192. 

Prototype  five  original  percepts,  95. 

Prototype  of  harmonic  forms  and  re- 
lations, 95, 

Prototype  of  harmonic  percept  and 
step  in  minor,  200. 

Prototype  major  harmonic  percept, 
200. 

Prototype  major  mode,  95,  180,  181, 

185,  191,  200,  214. 
Prototype  ninth,  208. 
Prototype  repose,  185. 
Prototype  upleader,  95,  192,  194. 

Rameau,  264. 
Regnant  bytone,  287. 
Regnant  dissonance,  127,  128. 
Regnant  dominant,  188,  207,  210. 
Regnant  harmony,  24,  25,  53,  54,  55, 


58,  60,  65,  67,  83-85,  88,  98,  104- 
113,  115-118,  125-127,  129-133, 
141,  149,  183-188,  193,  194,  198, 
201,  208,  209,  214,  220,  221,  223, 
224,  261-264,  267,  268, 272,  274-276, 
287. 

Regnant  harmony  in  one  voice,  102- 
133. 

Regnant  major  dominant,  188,  206, 
207. 

Regnant  major  subdominant,  188. 

Regnant  major  tonic,  108,  185. 

Regnant  minor  consonance,  218. 

Regnant  minor  dominant,  188, 206-218. 

Regnant  minor  subdominant,  188,  218- 
222. 

Regnant  minor  tonic,  199-206. 

Regnant  ninth,  210. 

Regnant  root,  208. 

Regnant  subdominant-harmony,  108. 

Regnant  third,  210. 

Regnant  tones,  106-112, 116-118, 120- 
123,  126,  193,  199,  207,  208,  210, 
211,  214,  216,  256,  261,  274,  287. 

Regnant  tonic-harmony,  102-133. 

Relation,  5,  6-9,  15,  17,  20-30,  41,  48, 
56,  58,  61,  64,  66,  75-81,  84-86,  89, 

92,  95,  99,  107,  110-112,  115,  120, 
123, 127-129, 133, 135, 136, 140, 143, 
152,  179,  182,  185,  186,  190-193, 
198,  200,  203,  205,  207,  211,  212, 
214,  233,  234,  248-251,  253,  255, 
256,  266,  276,  280,  281,  285,  286; 
elemental,  22, 23 ;  fifth-,  123, 249 ;  har- 
monic, 7,  22,  26,  27,  29,  35,  37-39, 
50,  60,  62,  65,  67,  76-78,  83,  87,  88, 

93,  100,  105,  106,  109,  111,  112,  119, 
122,  124,  141,  177,  247;  prototype 
harmonic,  95;  interval,  80;  inter- 
harmonic,  91,  93,  94;  key-,  60,  88; 
mode,  88,  91,  94,  108, 180;  prototype 
mode-,  185;  original  harmonic,  15,  26, 
27,  95, 107, 136;  rhythmic,  22,  44,  50, 
53,55,  103,  177;  rhythmo-harmonic, 
14,  23,  24,  98;  space-,  14,  22,  23,  30, 
38;  time-,  14,  22,  30,  38,  79,  104; 
tone-,  22,  24, 30,  42,  45, 48,  56,  58,  62, 


316 


INDEX 


67,  78, 89,  94,  98, 104,  180,  214,  224, 

278;  tonic  and  dominant,  196. 
Relation  of  cadence  and  repose,  44-47, 

50,  53,  55,  63,  85,  91,  98,  103. 
Relation  in  space  (harmony),  79. 
Report  (common,  harmonic,  self-),  19, 

112, 120, 179, 186,  195,  202,  220, 227, 

230 ;  common,  of  common  feeling,  17- 

22. 
Report  of  biad,  246,  247. 
Report  of  by  tone,  118, 119,  219. 
Report  of   chord,  134,  135,  138,  139, 

141,  233,  234,   245,  247,  255,  259, 

266. 
Report  of  common  feeling  and  percep- 
tion, 5,  19,  22,  24,  28,  45,  66,  69,  88, 

108,  135,  181,  230. 
Report  of  harmonic  numbers,  88,  283, 

284. 
Report  of  harmony,  24,  38,  47,  66,  67, 

85, 148,  209,  230,  262,  264,  276,  283. 
Report  of  homophony,  5,  6,  215,  230, 

232,  288. 
Report  of  melody,  108,  148-149,  176, 

179, 181, 182, 215,  216,  223, 224,  279, 

283,  284,  288. 
Report  of  mode,  215. 
Report  of  tone,  85,  89,   90,  135,   177. 

214,  216,  233,  246,  247. 
Report  of  triad,  232,  233,  248,  262. 
Repose,  41,  56,  61,  68,   92,  103,    116, 

123,  129,  130,    133,   142,  148,   177, 

178,   180,    185,   190,  214,   216,  223; 

rhythm-,  42-45,  50,  53,  67,  111,  120, 

121 ;  tone-,  45-48,  55,  62,  63,  67,  91, 

96-100,  121,  190-192,  201. 
Repose-harmony,  45-48,  62,  111. 
Repose-moment,  42,  44. 
Repose-thread   (of  harmony),   54,   55, 

67,  91,  97-99. 
Resolution,  48,  54,   55,  62,  64,  93,  96- 

98, 112,  113,  115,  135,  142,  152,  192, 

220.  235,  275. 
Rhapsody,  203. 
Rhythm,   1,  6-10,  12-14,  17,  20,  22- 

24,  28,  30,  33,  38,  48,  50-52,  54,  56, 

63.  65,  74,  79,  83,  89,  98-100,  103, 


104,  130,  148-153,  158,  160-163, 
171, 176, 180,  229,  286-289;  analysis 
of,  31-33;  =  balanced -motion,  10. 
30,  33,  38,  162;  cadence,  42-45,  50, 
53,  67,  111,  120,  121;  dual,  29,  32, 
43, 99, 173;  music-,  30,  32,  42,  50, 51, 
158,  165,  167,  171;  tone-,  7,  9,  10, 
14,  15,  29,  48,  152,  154,  155,  171, 
172;  triple,  29,  32,  99. 

Rhythm-numbers,  161. 

Rhythm-period,  12,  32,  33,  125,  127, 
129,  153,  193,  250,  286. 

Rhythm-repose,  42-44,  45,  50,  53,  67, 
111,  120,  121. 

Rhythmo-harmonic  accent,  25,  105. 

Rhythmo-harmonic  analysis,  289. 

Rhythmo-harmonic  content  of  melody, 
279,  288. 

Rhythmo-harmonic  equilibrium,  125. 

Rhythmo-harmonic  feeling,  278. 

Rhythmo-harmonic  form,  24,  279,  288. 

Rhythmo-harmonic  laws  of  causation, 
224. 

Rhythmo-harmonic  point,  25, 105. 

Rhythmo-harmonic  principles,  286. 

Rhythmo-harmonic  relation,  14,  23,  24, 
98. 

Rhythmo-harmonic  thought,  278. 

Rhythmo-harmonic  voice  of  music,  153, 
205. 

Richter  [Ernst  F.  E.],  249. 

Riemann,  181,  226,  230. 

Root,  25-27,  29,  30,  34-37,  40,  41,  47, 
51,  60,  61,  63,  67,  75-77,  80,  81,  84, 
85,  88-90,  93,  108,  113,  118,  123, 
142,  179,  180,  185,  189,  217,  223, 
227,  232,  234,  285,  287;  chord-,  135, 
136,  140,  232,  234,  237-243,  245, 
248,  249,  258-261,  268,  274,  275,  278; 
harmonic,  135,  136,  181,  189,  232, 
234,  258,  260,  272. 

Round-song,  181. 

Scale,  141,  142,  192,  205,  217,  230; 
ascending,  97,  228;  descending,  97, 
229;  diatonic,  144, 192;  Dorian-,  229; 
enharmonic,  215;  great,  64;  major. 


INDEX 


317 


26,  86, 143,  203;  mediant,  146;  melo- 
dic minor,  201,  203;  octonal,  144, 
146;  original,  of  the  tonic,  145;  pen- 
dant minor,  228;  pentatonic,  64,  65, 
109;  primitive,  64;  septonal,  146; 
small,  64;  supertonic-,  146;  tonic-, 
146;  Zarlino-Riemann,  228,  229. 

Scale-numbers,  86-88,  94. 

Scale  terminals,  143,  144. 

Schopenhauer,  14. 

Schumann,  49.  169,  171. 

Selection,  75,  140,  149,  183;  natural, 
17,  70,  71,  85;  personal,  70-72,  85, 
176,177,230. 

Sense,  harmonic,  69, 121, 147, 148,  182; 
music-,  165. 

Septimenaccord,  269. 

Septonate,  The,  24,  98,  104. 

Sequence,  6,  9,  25,  40,  51,  52,  60,  64, 
65,  102,  105,  181,  278. 

Seventh,  25-27,  29,  30,  41,  47,  61,  63, 
65,  67,  76-78,  81,  82,  85,  87,  89, 134, 
135,  137,  223,  268,  269,  287;  dimin- 
ished, 234;  harmonic,  234,  268,  269; 
minor,  76-78.  137;  small,  222,  223; 
thorough-bass,  268. 

Shaping  principle,  10,  11,  24,  28,  31- 
33,  36,  41,  48,  50,  51,  120,  130,  149, 
161,  162,  171-173,  195. 

Silence,  1,  7. 

Sixth,  36,  59, 138, 139. 

Sonata,  116,  155,  173,  174,  212,  266. 

Songs,  4, 15,  43,  53,  56,  157, 165;  bird, 
56.  58,  59,  61,  171,  176. 

Soprano,  287. 

Sound,  1,  7,  8,  21,  33,  34,  38,  43,  51, 
55,  165,  166. 

Space,  12-14,  22,  23,  30,  38,  79,  104, 
122, 150, 153. 

Spencer  [Herbert],  68. 

Step,  36,  59,  60,  64,  81,  87,  92,  93,  96, 
98, 112. 119. 125, 137,  138,  142, 144, 
145,  200,  209,  214,  228,  275. 

Strauss  [Richard],  171. 

Stringed  instrument,  166. 

Student,  39,  59,  73,  87,  93,  96,  99,  100, 
101,  139,  163,  164.  277,  279,   280, 


282-289;  work  for,  101,  164,    261, 

284,  286-288. 
Study  of  music,  1,  6,  21,  28,  289. 
Stumpf,  C,  21. 
Subbeat-period,  160. 
Subdominant,  144.  187.  188,  204,  253; 

regnant  minor,  218-220. 
Subdominant-harmony,  58,  60,  61, 108, 

198. 
Subdominant  seventh  chord,  254. 
Subdominant  triad,  235,  251,  262,  264. 
Subfix-tone,  257, 
Subharmony,  85,  88. 
Submediant,  144,  253,  263. 
Submediant  seventh-chord,   254,   256. 
Submediant  triad,  249-250,  256,   263. 
Subrhythm,    161-163,  167-170,     288; 

compound,  dual,  mixed,  triple,   286. 
Subsecond.  261,  268. 
Subsecond-chord,  261,  262,  265,  267- 

270. 
Subtonic,  144. 
Subtonic-chords,  253,  256. 
Subtonic   seventh-chord,    235,    254. 
Subtonic-triad,  251-253. 
Superfix-tone.  257. 
Supersixth.  261,  268. 
Supersixth  chord,  261-264,   267-270, 

271. 
Supertonic,  144,  253. 
Supertonic  seventh-chord,  254. 
Supertonic-triad.  251-253.  256. 
Syllables,  43,  61,  86-88,  94,  99,   100, 

144,  145,  186,  189,  229. 
Symbols,  30,  33,  61,  73,  86-89,  94, 135, 

145,  159,  161,  164,   180,  275,   276, 
279. 

Symphony,  116, 155, 173, 174,  212,  266. 
Syncopation,  169. 

Technique,  93,  100. 

Temperament,  95,  96. 

Tempo,  86. 

Tenor,  287. 

Tenths,  36. 

Tetrachord,  142-146, 200, 202, 208,  214. 

Tetrad,  269-272;  compound,  272. 


318 


INDEX 


Theme,  214. 

Theory,  3, 16, 17,  20,  22,  51,  52,  69,  70, 
89, 181,  200,  226-228,  233,  234,  244, 
269,  289;  acoustic,  230;  Zarlino- 
Riemann-,  181,  226,  230. 

Theory  of  pendant  minor,  226,  227. 

Third,  25-27,  29,  30,  34-37,  40,  41,  47, 
59-61,  63,  65,  67,  76,  81,  82,  85,  89, 
93, 108,  120,  137-139,  178,  179,  184, 
187, 189, 200,  206, 210,  211,  223,  224, 
285, 287;  double,  211,  212;  harmonic, 
135,  137,  234;  major,  34,  36,  61,  76- 
78,  81,  82,  120,  137,  138;  minor,  36, 
137,  138;  superadded,  257. 

Thirteenth,  82,  89. 

Thorough-bass,  259,  267,  269,  270,  274. 

Thread,  cadence,  of  harmony,  54; 
consonance,  37,  143;  dissonant,  143; 
dominant,  47,  82,  84;  harmonic,  35, 
36,  37,  38,  41,  54,  63,  79,  80,  81,  84, 
96,  107,  109, 124,  133, 134, 137,  139- 
141,  143,  178,  183,  188,  193,224; 
repose-,  54;  tonic-,  47,  59. 

Time,  clock,  174;  mathematical,  174 ; 
rhythmic,  174 ;  rhythmic  period  of,  38, 
42. 

Time-accent,  32. 

Time-period,  32,  33,  38. 

Time-relation,  14,  22,  30,  38,  79,  104. 

Tonality,  1.  39,  41,  56,  60,  61,  65,  67, 
77,  94-96,  103,  215,  224. 

Tone,  5-10,  13,  17,  25,  28,  29,  35-37, 
44,  46,  50,  53,  55,  74,  87,  88,  94-97, 
109,  112,  114,  117-119,  124,  127, 
133,  136-138,  140-142,  144,  148, 
153,  156,  165,  176,  182,  189,  190, 
192, 198,  201,  205, 206,  208,  210, 212, 
215, 228, 232, 233, 235,  239,  243, 247; 
accented  and  unaccented,  43;  added, 
262-264,  268,  274;  analysis  of,  33- 
35;  =balanced  sound,  30,  38;  bond-, 
63, 76, 122, 1 23, 285 ;  cadence-,  46, 47, 
67-59,  61-66,  92,  96-100,  106,  107, 
113,  135,  136,  191,  192,  235,  257; 
(prototype),  191, 194, 208 ;  chord-,  86 ; 
component,  85, 103, 106, 234 ;  elemen- 
tary, 34,  79;  =  equilibrium,  30,  125; 


harmonic  thread  of  a,  35-36 ;  hfirmo- 
nic,  38,  86;  harmonic  complex  of,  34, 
35, 37,  40, 41 ;  harmonic  pedigree,  224- 
231;  =  harmony,  30,  33;  infix,  257; 
initial,  247;  isolated,  34,  37,  40,  41, 
45,  55,  59,  60,  108, 177;  leading,  61 ; 
melodic-,  86;  mode-,  87,  93,  94;  origi- 
nal, 26,  27.  75,  76,  85,  107,  233; 
original  cadence-,  46, 92,  98, 106, 135, 
136;  original  repose-,  46;  physical, 
20;  pitching  a,  54;  regnant,  106-112, 
116-118,  120,  121,  123,  126,  193, 
199,  207,  208,  210,  211,  214,  216, 
256,  261,  274,  287;  repose-,  46,  62, 
63,  67,  86,  96-100,  257;  seventh,  82; 
seven  original,  26,  27,  75-86,  103, 
107,  225, 226;  single,  68,  79, 135, 139; 
stable,  257-260;  subfix-,  257;  super- 
fix-,  257;  terminal,  82;  thirteenth-, 
82;  three  stages  of,  193,  194;  un- 
stable, 257-260. 

Tone-cadence,  45-48,  55,  86,  91,  121. 

Tone-feeling,  28. 

Tone-genesis,  33,  51,  54,  95. 

Tone-material,    214,    220,    221,   257. 

Tone-moment,  23,  153. 

Tone-region,  141-149. 

Tone-relation,  22,  24,  30, 42,  45, 48,  56, 
58,  62,  67,  78,  89,  94,  98,  104,  180, 

214,  224,  278. 

Tone-repose,  45-47,  55,  62,  63,  67,  91, 

96-100,  190,  192,  201,  221. 
Tone-rhythm,  7,  9,  10-14,  15,  29,  48, 

152,  154,  155,  171,  172. 
Tone-system,  1,  27, 39,  65, 95, 147, 205, 

215,  224,  233. 

Tonic,  84,  90,  93,  229,  253,  272;  ma- 
jor, harmony,  33,  41,  45,  47,  54-61, 
63-65,  67,  77,  83,  84,  90-93,  98, 
103,  105-108,111,180,181,183-187, 
193,221,229,  260;  minor,  harmony, 
179, 180, 181, 184-187,  199-206, 214, 
221,  230;  rhythmic,  120. 

Tonic-centre,  143. 

Tonic-chord,  66. 

Tonic  components,  83. 

Tonic-root.  76. 


INDEX 


319 


Tonic-scale,  146. 

Tonic-septonate,  144,  145. 

Tonic-triad,  66,  84,  262,  268. 

Triad,  133,  134,  136,  139,  140,  255- 
241,  244,  248,  249,  264;  augmented, 
249, 262 ;  basic,  240 ;  diminished,  237, 
262;  gromid-,  238;  major,  90,  133, 
237,  251,  262,  268;  major  dominant-, 
84,  235,  249;  major  subdominant-, 
235,  264;  major  tonic-,  262,  268; 
mediant-,  248-250;  minor,  237,249, 
251,  262,  268;  minor  dominant-, 
235,  262;  minor  mediant-,  248,249, 
minor  subdominant-,  235,  262 ;  minor 
tonic-,  262,  268;  nucleus,  169,  262, 
263,  268,  269;  primary,  250,  251, 
253;  secondary,  249-251,  284;  sub- 
dominant-,  235,  251,  262,  264;  sub- 
mediant-,  249, 250, 256, 263 ;  sub-tonic, 
251-253;  supertonic,  251-253,  256; 
tonic-,  66,  84,  262. 

Triad  positions,  238-241, 

Tritonus,  144. 


Undertones,  227,  228. 

Upleader,  64,  92,  183,  208,  209,  239, 
285;  chromatic,  275;  major,  187, 
192;  minor,  187,  192;  prototype,  95, 
192,  194. 

Vierklang,  269. 

Voicing,  close  and  open,  267. 

Von  Biilow,  276. 

Wagner,  5,  49,  74,  140,  150,  171. 

Weber,  G..  50,  74. 

WeU-tempered  Clavichord,  170,  198. 

Wind  instruments,  166. 

Work    for    students,    101,    164,   282- 

288. 
World,  energy,  11,  12. 
World  equilibrium,  12. 
World  harmony,  12,  14. 
World  principle,  11. 
World  rhythm,  12. 

Zarlino,  181,  226,  230. 


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